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THE 


YOUNG  MILL. WRIGHT 


amiLa^^ 


IN  FIVE  PARTS. 


CONTAINING  :— 


Part  I. — Mechanics  and  Hydraulics ; 
showing  Errors  in  the  old,  and  esta- 
blisiiing-a  new  System  of  Theories 
of  Water- Mills,  by  which  the  power 
of  Mill-Seats,  and  the  effects  they 
will  produce,  may  be  ascertained  by 
calculation. 

Pabt  II. —  Rules  for  applying  the  The- 
ories to  practice ;  Tables  for  pro- 
portioning Mills  to  the  power  and 
fall  of  the  Water,  and  Rules  for 
finding  Pitch  Circles,  with  Tables 
from  6  to  136  cogs. 

Part  III  — Djrectionsfor  constructing 
and  using  all  the  Author's  patented 
Improvements  in  Mills. 


Part  IV. — The  Art  of  manufacturing 
Meal  and  Flour  in  all  its  parts,  as 
practised  by  the  most  skilfal  Mil- 
lers in  America. 

Part  V.— The  Practical  Mill- Wright; 
containing  instmctions  for  building 
Mills,  with  Tables  of  their  Propor- 
tions, suitable  for  all  Falls  from  3 
to  36  feet. 

Appendix. — Containing  Rules  for  dis- 
covering New  Improvemenis — ex- 
emplified in  Improving  the  Art  of 
cleaning  Grain,  hulling  Rice,  warm- 
ings Rooms,  and  venting  tjmoke  by 
Chimnies,  &c. 


EMBELLISHED  AVITH  TWENTY-FIVE  PLATES. 


BY  OLIVER  EVANS. 


FOURTH    EDITION. 

PHILADELPHIA : 

M.  CAREY  &  SON— CHESNUT  STREET. 


1831. 


DISTRICT  OF  PENNSYLVANIA— TO  wit: 

Be  It  R'^m  mbereil.  That  on  the  twenty  fifth  day  of  November,  in  the 

r  » thirty.'hird    year  of  the  Independence  of  the  United  Statt-s  of  America, 

OLIVKR  EVANS,  of  ihe  said  District,  halh  deposited  in  this   office  the 

title  of  a  book,  the  right  whereof  he  claims  as  Author  and  Proprietor 

in  the  following  words — to  wit: 

"  The  Young  Mill  Wright's  and  Miller's  Guide  In  five  parts.  Embel- 
lished with  twenty-five  plates,  8cc.  By  Oliver  Evans,  of  Philadelphia." 
In  conformity  to  the  Act  of  Congress  of  the  United  Slates,  intituled, 
"  An  Act  for  the  encouragement  of  learning,  by  securing  the  copies  of 
maps,  charts,  and  books,  to  the  authors  and  proprittors  of  such  copies, 
during  the  times  therein  mentioned." 

SAMUEL  CALDWELL, 
Clerk  of  the  District  of  Pennsylvania. 


PREFACE. 


The  reason  why  a  book  of  this  kind,  although 
so  much  wanted,  did  not  sooner  appear,  may  be 
— because  they  who  have  been  versed  in  science 
and  literature,  have  not  had  practice  and  experi- 
ence in  the  arts ;  and  they  who  have  had  prac- 
tice and  experimental  knowledge,  have  not  had 
time  to  acquire  science  and  theory,  those  neces- 
sary quahtications  for  completing  the  system,  and 
which  are  not  to  be  found  in  any  one  man.  Sen- 
sible of  my  deficiencies  in  both,  I  should  not  have 
undertaken  it,  was  I  not  interested  in  the  explana- 
tion of  my  own  inventions.  I  have  applied  to 
such  books  and  men  of  science  as  I  expected  as- 
sistance from,  in  forming  a  system  of  theory ;  and 
to  practical  mill-wrights  and  millers  for  the  prac- 
tice ;  but  finding  no  authors  who  had  joined  prac- 
tice and  experience  with  theory,  (except  Smeaton 
whom  I  have  quoted)  finding  many  of  their  theo- 
ries to  be  erroneous,  and  losing  the  assistance  of 
the  late  ingenious  William  Waring,  the  only  sci- 
entific character  of  my  acquaintance,  who  ac- 
knowledged that  he  had  investigated  the  principles 
and  powers  of  water  acting  on  mill-wheels,  I  did 
not  meet  the  aid  1  expected  in  that  part. 

Wherefore  it  is  not  safe  to  conclude  that  this 
work  is  without  error — but  that  it  contains  many. 


IV  PREFACE. 

both  theoretical,  practical,  and  grammatical ;  is 
the  most  natural,  safe,  and  rational  supposition. 
The  reader,  whose  mind  is  free  and  unbiassed  by 
the  opinion  of  others,  >vill  be  most  likely  to  attain 
the  truth.  Under  a  momentary  discouragement, 
finding  I  had  far  exceeded  the  prescribed  limits, 
and  doubtful  what  might  be  its  fate,  I  left  out  se- 
veral expensive  draughts  of  mills,  ^c.  But  since 
it  went  to  press  the  prospects  have  become  so  en- 
couraging that  I  may  hope  it  will  be  well  received: 
Therefore  I  request  the  reader,  who  may  prove 
any  part  to  be  erroneous,  can  point  out  its  defects, 
propose  amendments,  or  additions  ;  to  inform  me 
thereof  by  letter ;  that  T  may  be  enabled  to  cor- 
rect, enrich,  and  enlarge  it.  in  case  it  bears  another 
edition,  and  I  will  gratefully  receive  their  commu- 
nications :  For  if  what  is  known  on  these  subjects 
by  the  different  ingenious  practitioners  in  America 
could  be  collected  in  one  work,  it  would  be  pre- 
cious indeed,  and  a  sufficient  guide  to  save  thou- 
sands of  pounds  from  being  uselessly  expended. 
For  a  work  of  this  kind  will  never  be  perfected  by 
th»*  abilities  and  labours  of  one  man. 

The  practical  part  received  from  Thomas  Elli- 
cottwill  doubtless  be  useful,  considering  his  long 
experience  and  known  genius. 

Comparing  this  with  other  oridnal,  difficult 
works,  with  equally  expensive  plates,  the  price 
will  be  found  to  be  low. 


CONTENTS. 


PART  I. 

MECHANICS. 

Articles, 

1.  \xioMs,  or  self  evident  truths         .-.-..-      Page  9 

2.  Of  the  first  principles  of  mechanical  motion              ...        -  10 
S.  —  elasticity,  its  power  unknown              ..--.-  H 

4.  —  motion,  absolute  and  relative              .--.-.  12 

5.  —  do.  accelerated  and  retarded               -«--.-  IS 

6.  —  the  momentum  or  quantity  of  motion          -         .        -        .        .  13 

7.  —  general  laws  of  motion        ..--..--  15 

8.  —  the  momentum  of  clastic  and  non-elastic  bodies  in  motion             -  16 

9.  —  laws  of  motion  and  force  of  falling  bodies ;  table  and  scale  of  their 

motion  .-..--.  20 
10.  —  the  laws  of  motion  of  bodies  descending  inclined  planes,  and  curved 

surfaces    --------  25 

12    —  the  motion  of  projectiles     ------  26 

13.  —  circular  motion  and  central  forces              _            .            -            -  27 

14.  —  centres  of  motion,  magnitude  and  gravity              -            -            -  30 

15.  —  general  laws  of  mechanical  powers             _             -             .             _  31 
16 — 21.  OF  levers,  simple    and  compound ;  their  laws  applicable  to   mill- 
wheels  ;  general  rule  for  calculating  their  power             -            -  33 

21.  Power  decreases  as  the  motion  increases         -             -             -             .  39 
22 — 23.  No   power  gained  by  enlarging  undershot-wheels,  nor  by  double 

gearing  mills  .----.-  39 
24.  The  pulley,  25  the  axk  and  wheel,  26  the  inclined  plain,  27  the  wedge, 

and  28  the  screw  _-_...  4I 
30.  The  fly-wheel,  its  use  ..----  45 
31 — 33.  Of  friction,  its  laws,  and  the  inventions  to  reduce  it  -  -  46 
34.  Of  maximums,  or  the  greatest  eflFect  of  machines  -  -  -  50 
35 — 37.  Old  theory  of  the  motion  of  undershot-wheels  investigated ;  new  the- 
ory proposed;  scale  of  experiments  -  -  -  -  51 
38 — 39.  William  Waring's  new  theory        -----  60 

40.                  ■        theory  doubted              -            -            .            -  64 

41 — 42.  Search  for  a  true  theory  on  a  new  plan,  and  one  established  agreeing 

with  practice  -------65 

43 — 44.  The  maximum  motion  of  overshot-wheels,  with  a  scale  thereof    -  74 

HYDRAULICS. 

45 — 47.  Laws  of  the  motion  and  effects  of  spouting  fluids ;  their  application 

to  undershot-mills              ...           -            -            -  79 


VI  GONTENTS. 

Articles,  Pagp 
48 — 50.  Hydrostatic  paradox ;  on  which  is  founded  a  theorem  for  finding  the 

pressure  of  wattf  on  any  surface                -            -            -            -  85 

51.  Rule  for  finding  the  velocity  of  spouting  water              ...  87 

52.  Rule  for  finding  the  effect  of  any  gate  of  water  on  undershot-wheels  8f 
53 — 54.   Water  applied  by  gravity  ;  the  power  thereof  on  the  principles  of 

overshot-mills.  equal  in  theory  to  the  best  application  possible     -  90 

55.  Friction  of  the  aperture  on  spouting  fluids           -           -             -             -  94 

56.  Pressure  of  the  air  the  cause  of  fluids  rising  in  pumps  and  cyphons,  &c.  95 

57.  Directions  for  pump-makers,  with  a  table           -             -             -             -  97 

58.  Tubes  for  conveying  w^ater  over  hills  wnd  under  valleys            -            -  99 

59.  Paradoxical  mill  explained,  that  will  not  move  empty;  the  difference  of 

force  of  indefinite  and  definite  quantity  of  water                 -             -  99 

60.  The  motion  of  breast  and  pitch-back  wheels.  They  do  not  run  before  the 

gravity  of  the  wHtei- on  account  of  the  impulse         -         -             -  101 

61.  Simple  rule  for  calculating  the  power  of  a  mill-seat        -        -            -  104 

62.  Theory  compared,  with  a  table  of  experiments  of  18  mills  in  practice, 

and  found  to  agree           .---.-  108 

63.  Rules  for  proportioning  the  size  of  mill- stones  to  the  power ;  with  a  table 

of  their  areas,  powers  required,  and  quantity  ground,  &c.           -  110 

The  surface  passed  by  mill-stoues  of  different  size  and  motion             -  115 

C4 — 65.  Of  digging  canals;  with  their  proper  fall  and  size  to  suit  the  stones  117 

65.  Of  air-pipes,  to  prevent  trunks  from  bursting              .             -             -  12# 

67.  Smeaton's  experiments  concerning  undershot-mills                 -            -  121 

68.  ——— experiments  concerning  OMTshot-mills        -           -            -  137 
89.  __—  experiments  concerning  wind-mills            -             -            _  144 

PART  II. 

70.  Of  undershot-mills,  with  a  table  containing  the  motion  of  the  water  and 

wheels,  and  proportion  of  the  gears,  suitable  to  any  hi-ad  from  1  to 
25  feet,  both  double  and  single  gear;  the  quantity  of  water  required 

to  turn  them,  and  the  size  of  the  gate  and  canal              -            -  155 

71.  Of  tub  mills,  with  a  table  showing  the  diameter  of  the  wheels  to  suit  any 

size  stone,  or  head  of  water          -            -            -            -            -  1C§ 

72.  Of  breast  and  pitch -back  wheels,  with  a  table  complete  for  them       -  165 

73.  Of  overshot-mills,  with  tables  for  them            -            -            -            .  171 
Of  mills  moved  by  re-action     ------  17S 

74.  Rules  for  calculating  the  motion  of  wheels,  and  number  of  cogs  to  pro- 

duce ih^  desired  motion               .            .            _            _            -  175 

75.  Rules  for  finding  the  pitch  circles        -            -            .            ,            .  I8I 

76.  A  true,  simple,  and  expeditious  method  for  finding  the  diameter  of  the 

pitch  circle,  with  a  table  showing  the  diameter  of  pitch  circles,  &c.  182 

77.  Rules  for  measuring  garners,  hoppers,  &c.         -                        -            -  18S 

78.  Of  the  different  kind  of  gears  and  forms  of  cogs            .            -            _  i8g 
79 — 81.  Of  spur,  face,  and  bevel  gears        -----  igg 

82.  Of  matching  wheels,  to  make  them  wear  even  and  well            -            -  194 

83.  Theories  of  rolling-screens  and  fans  for  cleaning  the  grain,  improved  ap- 

plication of  them    -------  195 

84.  Of  gudgeons,  the  cause  of  their  heating  and  getting  loose,  with  the  reme- 

dies therefor  -  -  -  -  -  -  -197 

55.  On  building  mill-dams                --....  2OO 

56.  On  laying  foundations  and  building  mill-walls               -            _            _  202 


CONTENTS.  Vll 


PART  III. 

Article!,  Page 

8".  General  account  of  the  new  improvements        .             .            -            .  207 

88.  Particular  dt-scriptioii  of  the  machines               >            _            -            -  209 

89.  Application  of  the  machines  in  the  process  of  manufacturing  flour         -  213 

90.  Of  elevating  grain  from  ships        -          -            -            -            -  ■          i  216 

91.  .\  mill  for  grinding  parcels          -..---  217 

92.  A  grist-mill  improved         .-.-.--  219 

93.  Of  elevating  from  ships  and  storehouses  by  a  horse       .            -            -  221 

94.  Of  an  elevator  wrought  by  a  man           -            -            -            -            -  222 

95.  Construction  of  the  wheat  elevator,  particularly  directed            -             -  226 
96 — 100.  Of  the  meal  elevator,  the  meal  conveyer,  the  grain  conveyer,  the 

hopper-boy,  and  the  drill        -        -            -            -            -            -  233 

101    Of  the  utility  of  the  machines                .            .            -            -            ■  242 

102.  Bills  of  materials,  both  of  wood  and  iron,  &c.  to  be  prepared  for  building 

the  machines              ...----  246 

103.  A  mill  for  hulling  and  cleaning  rice       -----  249 

PART  IV. 

104.  The  principles  on  which  grinding  is  performed,  explained        -            -  257 

105.  Of  the  draught  necessary  to  be  given  to  the  furrows  of  mill-stones       -  260 

106.  Directions  for  facing  new  mill-stones        -----  264 

107.  Of  hanging  mill-stones       -..--.-  266 

108.  Of  regulating  the  feed  and  water  in  grinding                 ...  268 

109.  Rules  for  judging  of  good  grinding         .            -            .            -            _  269 

110.  Of  dressing  and  sharpening  the  stones  when  dull           -            -            .  270 

111.  Of  the  most  proper  degree  of  fineness  lor  flour             -            -            -  271 

112.  Of  garlic,  with  directions  for  grinding  wheat  mixed  therewith;  and  for 

dressing  the  stones  suitable  thereto                -             -             .             -  273 

113.  Of  grinding  over  the  middlings,  stuff"  and  bran,  or  shorts,  if  necessary, 

to  make  the  most  of  them         ------  275 

114.  Of  the  quality  of  the  mill-stones,  to  suit  the  quality  of  the  wheat          -  277 

115.  Of  bolting-reels  and  cloths,  with  directions  for  bolting  and  inspecting 

flour              ---.--..  280 

116.  Directions  for  keeping  the  mill,  and  the  business  of  it,  in  good  order  -  283 

117.  Peculiar  accidents  by  which  mills  are  subject  to  catch  fire         -            -  284 

118.  Observations  on  improving  of  mill-seats             -            -            -            -  285 

PART  V.     [See  the  contents  at  the  beginning  of  it.] 

CONTENTS  OF  THE  APPENDIX. 

Rules  for  discovering  new  improvements,  exemplified. — I.  In  Cleaning  grain  by 
wind.  II.  Distillation  of  spiiits.  III.  Inventing  smoke  from  rooms  by  chim- 
neys. IV.  Warming  rooms  by  fire  to  save  fuel.  V.  Hulling  and  cleaning  rice. 
VI.  Saving  ships  from  sinking  at  sea.  VII.  Preserving  fruits  and  liquors  from 
.putrefaction  and  fermentation. 


VHl  CONTENTS. 

EXPLANATION  OF  THE  TECHNICAL  TERMS,  kc. 
USED  IN    iHIS  WUKK. 

aperture,  The  opening  by  which  water  issues. 

^rea.  Plane  suiface,  superficial  contents. 

Atmosphere,  The  surrounding  air. 

Mgebruic  djmis  used  are  _^  for  more,  ar  addition.  —  Less,  subtracted,  y^  Mul- 
tiplication ^  Division.  ^^  Equality.  ^  The  square  root  of  863  for  86 
squired,  883  for'  88  cubed. 

Biquudrate,  A  number  twice  squared  :  the  biquadrate  of  2  is  16. 

Corollurij,  Inference. 

Cuboch,  A  name  for  the  unit  or  integer  of  power,  being  one  cubic  foot  of  water 
multiplied  into  one  foot  perpendicular  descent. 

Cubic  fo':t  (ijioater.  What  a  vessel  one  foot  wide  and  one  foot  deep  will  hold. 

Cvbe  of  a  number.  The  product  of  the  number  multiplied  by  itself  twice. 

Cube  root  of  a  number.  Say  of  8,  is  the  number,  which  multiplied  into  itself  twice 
will  produce  8,  viz.  2.    Or  it  is  that  number  by  which  you  divide  a  number  twice 
to  quote  itself. 
Decimal  point,  set  at  the  left  hand  of  a  figure  shows  the  whole  number  to  be  di- 
vided into  tens,  as  ,5  for  5  tenths;  ,57  for  57  hundredths;  ,557  for  557  thousandth 
parts. 
Eq^nlibrio,  Equilibrium. — Equipoise,  or  balance  of  weight. 
Elastic.  Springing. 
Friction,  The  act  of  rubbing  together. 
Gravity,  That  tendency  all  matter  has  to  fall  downwards. 
Hydrostatics,  Science  of  weighing  fluids. 
Bydruidics,  Water-works,  the  scierice  of  motion  of  fluids. 
Impulse,  Force  communicated  by  a  stroke. 
Impetus,  Violent  effort  of  a  body  inclining  to  move. 
Momentum,  The  force  of  a  body  in  motion. 
Maxivmm,  Greatest  possible. 
J^'owelastic,  Without  spring. 

Ocmble,  Eight  limes  told. 

Paradox,  Contrary  to  appearance. 

P'.icussiun,  Striking  a  stroke,  impulse. 

Problem,  A  question. 

Qnadmiple,  Four  times,  fourfold. 

Radius,  Hiilf  the  diameter  of  a  circle. 

Sipht  angle,  A  line  square,  or  perpendicular  to  another. 

Squared,  Multiplied  into  itself;  -2  squared  is  4. 

Theory,  Speculative  plan  existing  only  in  the  mind. 

Tangent,  A  line  perpendicular  or  square  with  a  radius  touching  the  periphery  qf  a 

circle. 
Theorem,  Position  of  an  acknowledged  truth. 
Velocity,  Swiftness  of  motion. 
Virtual  or  effective  descent  of  -water :    See  Art.  61. 

SCALE  FROM  WHICH  THE  FIGURES  ARE  DRAWN. 

PLATE  11    Fig.  1 1 ,  12,  8  feet  to  an  inch ;  fig.  19,  10  feet  to  an  inch. 
HI.  Fig.  19,  20,  23,  86,  10  feet  to  do. 
IV.  Fig.  28.  29,  30,  31 ,  32,  33,  10  feet  do. 

VI.  Fig.  I,  lOfeettoaninch;  fig.  2,  3,  8,9, 10,  11,  2  feet  do. 

VII.  Fg.  12.  13,14,  15,  two  feet  to  an  inch;  fig.  16,  10  do. 

X.  F;g.  1,  2,  18  feet  do.  fig.  H,  I  in  fig.  1 ,  four  feet  to  ao  iaiA, 

XI.  Fig.  1, 2, 3,  two  feet  do.  fig.  6,  8,  one  foot  to  de. 


THE 

YOUNG    MILL-WRIGHT'S 


AND 


MILLER'S   GUIDE. 


PART  THE  FIRST. 
CHAPTER  L 

ARTICLE    1. 

OP  THE  FIRST  PRINCIPLES  OF  MECHANICS. 

MOTION  may  be  said  to  be  the  beginning  or 
foundation  of  all  mechanics ;  because  no  mechanical 
operation  can  be  performed  without  motion. 

AXIOMS ;  or,  Self-evident  Truths, 

1.  A  body  at  rest  will  continue  so  for  ever,  unless  it  is 
put  in  motion  by  some  force  impressed.* 

2.  A  body  in  motion  will  continue  so  for  ever,  with  the 
same  velocity  in  the  same  direction,  unless  resisted  by 
some  force. t 

3.  The  impulse  that  gives  motion,  and  the  resistance 
that  destroys  it,  are  equal. 

*  This  sluggish,  inactive  principle,  or  resistance,  by  which  a  body  in- 
clines to  a  state  of  rest,  is  called  Inertia. 

t  The  same  principle  of  inertia,  which  inclines  a  body  to  remain  atrest« 
also  inclines  it  to  continue  in  motion  for  ever,  if  once  put  in  motion,  and 
that  in  a  right-lined  direction,  unless  changed  by  some  force  :  therefore  no 
body,  moving  in  a  straight  line,  can  be  turned  into  a  curve  line,  but  by 
some  force  ;  the  consideration  of  which  may  lead  us  to  the  knowledge  of 
the  true  principles  of  some  mills.    See  the  latter  part  of  art,  7o. 

B 


1©  MECHANICS.  [Chap.  1. 

4.  Causes  and  effects  are  equals  or  directly  propor- 
tional. 

POSTULATUMS ;   or,  Positions  without  Proof. 

A  quadruple  impulse,  or  moving  power,  is  requisite 
to  communicate  double  velocity  to  a  body  ;*  therefc^re 
a  quadruple  resistance  is  requisite  to  destroy  double 
velocity  in  a  body,  by  axiom  3d. 

The  impulse  we  may  call  power,  and  the  resistance 
that  it  overcomes,  the  effect  produced  by  that  power. 

COROLLARY. 

Consequently,  the  powers  of  bodies  in  motion,  to- pro- 
duce effects,  are  as  the  squares  of  their  velocities  ;  that  is, 
a  double  velocity,  in  a  moving  body,  produces  four  times 
the  effect. 


ART.    2. 

OF  THE  PRINCIPLES  OF  MECHANICS. 

There  are  two  principles  which  are  the  foundation  of 
all  mechanical  motion  and  mechanical  powers,  viz.  Gra- 
vity and  Elasticity  ;  or.  Weight  and  Spring. 

By  one  or  the  other  of  tliese  principles  or  pow'ers,  every 
mechanical  operation  is  performed. 

Gravity,  in  the  extent  of  the  word,  means  every  species 
of  attraction  ;  but  more  especially  that  species  which  is 
common  to,  and  nmtual  between,  all  bodies  ;  and  is  evi- 
dent l^etween  the  sun  and  its  planetary  attendants,  as  also 
the  earth  and  the  moon.f     But  we  will  only  consider  it, 

*  In  the  course  of  this  work,  I  shall  shew,  that  a  quadruple  impulse 
produces  onlv  double  velocity.  See  art.  7  ami  46.  We  should  folio  >•  phi- 
losophers only  in  the  p^ths  of  truth  ;  because,  if  all  men  are  subject  ta 
err,  even  the  most  eminent  philosophers  may  have  erred. 

If  a  thf-ory  will  not  at^ree  with  practice,  we  may  suspect  it  is  not  true; 
and  the  theory  of  tlie  momentum,  or  force  of  bodies  in  motion,  beinj^-  as  their 
velocities  simply,  does  not  agree  with  practice,  with  respect  to  the  effects 
they  produce,  either  in  circular  motion,  art.  13,  falline^  bodies,  art.  9, 
spoutingr  fluids,  art.  45,  wind  on  mill  sails,  art.  69,  therefore  we  have  rea- 
son to  suspect  that  this  theory  may  not  be  true,  in  every  respect. 

f  It  is  this  attraction  of  gravity  between  the  heavenly  bod. es,  that  keeps 
up  the  order  of  their  motion,  in  their  revolution  round  each  other.  See 
Ferguson's  Lectures,  page  23- 


Chap.  1.]  MECHANICS.  1^ 

as  it  relates  to  that  tendency  which  all  bodies  on  the  earth 
have  to  fall  towards  its  centre ;  thus  far  it  concerns  ths- 
mechanical  arts,  and  its  laws  are  as  follows,  viz.  : 


Laxvs  of  Gravity. 

1.  Gravity  is  common  to  all  bodies,  and  mutual  be 
tween  them. 

2.  It  is  in  proportion  to  the  quantity  of  matter  in  bo- 
dies. 

3.  It  is  exerted  every  way  from  the  centre  of  attracting 
bodies,  in  ris^ht- lined  directions  ;  therefore  all  bodies  on 
the  earth  tend  to  the  centre  of  gravity  of  the  earth.* 

4.  It  decreases  as  the  squares  of  the  distance  increase ; 
that  is,  if  a  body.,  on  the  earth,  was  to  be  removed  to 
double  the  distance  from  the  centi-e  of  gravity  of  the  eardi, 
about  4000  miles  high,  it  would  there  have  but  one- 
fourth  of  the  gi'avity  or  weight  it  had  when  on  the  ground : 
but  a  small  height  from  the  surface  of  the  earth  (50,  or 
100  feet)  makes  no  sensible  difference  in  gravity.f 

By  the  3d  law,  it  follows,  that  all  bodies  descending 
freely  by  their  gravity,  tend  towards  the  earth,  in  right 
lines,  perpendicular  to  its  surface,  and  with  equal  velo- 
cities (abating  for  the  resistance  of  the  air)  as  is  evident 
by  the  2d  law.:j: 

*  The  centre  of  gravity  of  a  body,  is  that  point  on  which,  if  the  body 
be  suspended,  it  will  remain  at  rest  in  any  posiiion  ;  or,  it  is  the  centre 
of  the  whole  weight  or  matter  of  the  body.     Art  14 

f  The  diameter  of  the  earth  is  allowed  to  be  ahout  8000  miles;  there- 
fore  we  may  suppose  the  centre  of  gravity  of  the  earth  to  be  about  4000 
miles  from  its  surface;  and  any  sm  11  distance  from  its  surface,  such  as 
one  mile  high,  wdl  make  no  sensible  difference  in  gravity.  But  when  the 
distance  is  so  great  as  to  bear  a  considerable  proportion  to  the  distance  of 
the  centre  of  gravity  of  the  earth,  then  the  power  of  gravity  will  decrease 
sensibly.  Thus,  at  the  distance  of  the  movXi,  which  at  a  mean,  is  about 
60  semi-diameters  of  the  earth,  the  power  of  gravity  is  to  that  on  the  sur- 
face of  the  earth,  as  1  to  3600-     See  Martin's  Philosophy. 

\  This  resistance  will  be  as  the  surface'-  of  the  bodies;  therefore  the 
smaller  the  body  of  equal  matter,  the  greater  will  be  the  velocity  of  its 
fall.  But  it  has  been  proved,  by  experiment,  that  a  feather  w;ll  fall  with 
the  same  velocity  as  a  guinea,  in  vacuo-    See  Ferguson's  Lectures,  p.  183. 


12  MECHANICS^  [Chap.  1. 


ART.    3. 

ELASTICITY. 

Elasticity  is  that  strength  or  repulsive  power,  which 
any  bcidy  or  quantity  of  matter,  being  confined  or  com- 
pressed, has  to  expand  itself;  such  as  a  spring  that  is 
bent  or  wound  up,  heated  air  or  steam  confined  in  a  ves- 
sel, &c.  and  by  it  many  mechanical  operations  are  per- 
formed. 

Elasticity,  in  the  full  sense  of  the  word,  here  means 
every  species  of  repulsion. 

The  limits  of  the  prodigious  power  of  repulsion  which 
takes  place  between  the  particles  of  heated  air  and  steam, 
are  not  yet  known.  Their  effects  are  seen  in  the  ex- 
plosion of  gunpowder,  the  bursting  anjd  cracking  of  wood 
in  the  fire,  &c.  In  short,  in  every  instance,  where  steam 
could  not  find  room  to  expand  itself,  it  has  burst  the  ves- 
sel that  confined  it,  endangering  the  lives  of  those  who 
were  near  it.* 

Having  premised  what  was  necessary  to  the  right  un- 
derstanding of  the  science  of  mechanics,  which  mostly 
depends  upon  the  principles  of  gravitation. 

We  come  to  consider  the  objects  thereof,  viz.  the 
nature,  kinds,  and  various  effects  of  motion  and  moving 
bodies,  and  the  structure  and  mechanism  of  all  kinds  of 
machines,  called  mechanical  powers,  whether  simple  or 
compound. 

•  A  worthy  and  ing'enious  young  man,  having  prepared  a  vessel  of 
wrout^ht  iron,  about  3  indies  diameter,  and  9  inches  long,  partly  filled 
Willi  water,  had  put  it  into  a  smith's  fire,  and  was  trymg  some  experiments, 
when  tlie  aperture,  by  which  the  steam  was  meant  to  issue,  got  stopped  by 
some  means  (as  is  supposed)  and  the  vt^ssel  burst  with  noise  like  a  can- 
non, carried  off  his  right  arm,  and  left  it  laying  across  one  of  the  upper 
beams  of  the  shop,  and  otherwise  desperately  wounded  him.  This  pro- 
digious power  is  applied  to  raise  water  out  of  coal  mint  s,  &c-  from  great 
depths,  in  surprising  quantities,  and  to  turn  mills  :  it  may  (m  my  opinion), 
be  applied  to  many  other  useful  purposes,  which  it  is  not  yet  applied  to. 

On  tiiis  subject  mucii  might  be  said  ;  but  as  it  does  not  immediately 
concern  this  work,  perhaps  1  have  said  enough  to  excite  the  reader  to  pe- 
ruse the  several  late  authors  on  philosophy,  who  have  treated  largely  on 
it,  and  to  tliem  I  must  refer.  Also  to  my  new  work  entitled  The  Abor- 
tion of  the  Young  Steam-engineer's  Guide. 


€hap.  2.]  MECHANICS.  13 

CHAPTER  n. 

ART.    4. 

OF  MOTION   AND  ITS  GENERAL  LAWS. 

MOTION  is  the  continual  and  successive  change  of 
space  or  place,  and  is  either  absolute  or  relative. 

Absolute  motion  is  the  change  of  space  or  place  of 
bodies,  such  as  the  flight  of  a  bird,  or  the  motion  of  a  ball 
projected  in  the  air. 

Relative  motion  is  the  motion  one  body  has  with  re- 
spect to  another,  such  as  the  difference  of  motion  of  the 
flight  of  two  birds,  or  of  two  ships  sailing.* 


ART.    5. 

Motion  is  either  equable,  accelerated,  or  retarded. 

Equable  motion  is  when  a  body  passes  over  equal 
distances  in  equal  times. 

Accelerated  motion,  is  that  which  is  continually  in- 
creased ;  such  is  the  motion  of  falling  bodies. f 

Retarded  motion,  is  that  which  continually  decreases; 
such  is  the  motion  of  a  cannon  ball  thrown  perpendicu- 
larly upwards.^ 

*  If  two  ships,  A  an;l  B,  move  with  the  same  velocity,  in  the  same  di- 
rection,  thtn  their  absolute  motion  is  the  same,  and  they  liave  no  relative 
motion,  and  neither  of  them  will  appear  to  a  person  on  board  of  ihe  other 
to  move  at  all.  Hence  it  is,  that  although  the  earth  is  continually  revolv- 
ing about  its  axis,  with  a  velocity,  at  the  equator,  of  about  1042  miles  ia 
an  hour,  and  round  the  sun,  in  continual  absolute  motion,  with  a  velocity 
of  about  58,000  miles  tn  an  hour — yet,  as  all  -bjects  on  its  surface  have 
the  same  absolute  motion,  they  appear  to  be  at  rest,  and  not  to  move  at 
all :  therefore  all  motion  of  bodies  on  the  earth,  appears  to  us  to  be  ab- 
solute motion,  when  compared  with  the  objects  fixed  on  the  earth;  yet,  if 
we  take  into  consideration  the  absolute  motion  of  the  earth,  all  motion  on 
it  will  appear  to  be  merely  relative. 

If  two  ships,  A  and  B,  moving'  with  equal  velocities,  pass  each  other, 
then  they  will  appear,  to  a  spectator  on  board  of  either,  to  move  with  dou- 
ble their  respective  real  velocities. 

Hence  the  reason,  why  a  person,  ridini^  against  the  wind,  finds  its  force 
greater,  and  with  it,  its  force  less,  than  it  really  is. 

+  A  falling  body  is  constantly  acted  upon  by  all  the  powerof  its  own  gra- 
vity;  therefore  its  motion  is  continually  increased. 

t  A  cannon  ball,  projected  perpendicular  tipwards,  is  constantly  resisted 
by  the  whole  power  of  its  own  gravity ;  therefore  its  motion  will  be  conti- 


14  MECHANICS.  [Chap.  2 


ART.    6. 

The  momentum  or  quantity  of  motion,  is  all  the  power 
or  force  which  a  moving  body  has  to  strike  an  obstacle  to 
produce  effects,  and  is  equal  to  that  impressed  force  by 
which  a  body  is  compelled  to  change  its  place,  by  axiom 
3,  art.  1  ;  \a  hich,  I  think,  ought  to  be  distinguished  by 
two  names,  viz.  instant  and  effective  momentums. 

1.  The  instant  momentum,  or  force  of  moving  bodies, 
is  in  the  compound  ratio  of  their  quantities  of  matter  and 
simple  velocities  conjointly ;  that  is,  as  the  weight  of  the 
body  A,  multiplied  into  its  velocity,  is  to  the  weight  of 
the  body  B,  multiplied  into  its  velocity,  so  is  the  instant 
force  of  A  to  the  instant  force  of  B.  If  A  has  4lbs.  of 
matter,  and  1  degree  of  velocity,  and  B  has  21bs.  of  mat- 
ter, and  4  degrees  of  velocity ;  then  the  momentum  of 
their  strokes  will  be  as  4  is  to  8  ;  that  is,  supposing  them 
to  be  instantaneously  stopped  by  an  obstacle. 

2.  The  effective  momentum,  or  force  of  moving  bo- 
dies, is  all  the  effect  they  will  produce  by  impinging  on 
any  yielding  obstacle,  and  is  in  the  compound  duplicate 
ratio  of  iheir  quantities  (or  weights)  multiplied  into  the 
squares  of  their  velocities  ;  that  is,  as  the  weight  of  the 
body  A,  multiplied  into  the  square  of  its  velocity,  is  to  the 
weight  of  the  body  B,  muliplied  into  the  square  of  its 

nually  decreased,  and  totally  stopped  as  soon  as  the  sum  of  this  resistance 
amounts  to  the  first  impulse,  by  axiom  3d,  art-  1,  when  it  will  begin  to  de- 
scend, and  its  motion  wdl  be  continually  increased  by  the  same  power  of 
its  own  gravity  :  its  motion  downwards  will  be  equal  to  its  motion  up- 
wards, in  every  part  of  its  path,  and  will  return  to  the  mo.ith  ot  the  can- 
non with  the  velocity  and  force  that  it  left  it ;  and  the  time  of  its  ascent 
and  descent  will  be  equal,  supposing  there  was  no  resistance  from  the  air 
— but  this  resistance  will  make  a  considerable  difference 

From  this  prmciple  of  a -celerated  motion  in  falling  bodies,  may  appear 
the  reason,  why  water  po'ired  from  the  spout  of  a  tea-kettle,  will  not  con- 
tinue in  a  stream  farther  than  about  two  feet,  and  this  stream  becomes 
smaller  as  it  approaches  the  place  where  it  breaks  into  drops  ;  because  the 
attraction  of  cohesion  keeps  the  water  together,  until  the  accelerated  mo- 
tion of  its  fall,  which  stretches  the  stream  smaller  and  smaller,  overcomes 
the  ohesion,  and  then  it  breaks  into  drops,  and  these  drops  become  fur- 
ther asunder  whde  they  continue  to  fall;  therefore,  if  the  clouds  were  to 
empty  themselves  in  torrents,  the  water  would  fall  on  the  ear'h  in  drops. 
This  may  serve  to  shew  the  disadvantage  of  drawing  the  gate  of  a  water- 
mdl  at  a  great  distance  from  the  float-board,  but  more  of  this  hereafter. 
See  art.  59. 


Chap.  2.]  MECHANICS.  15 

velocity,  so  is  the  effective  momentum  of  A  to  that  of  B. 
If  A  has  21bs.  of  matter  and  2  degrees  of  velocity,  and  B 
21bs.  of  matter  and  4  degrees  of  velocity,  then  their  ef- 
fective momentums  are  as  8  to  32 ;  that  is,  a  double  ve- 
locity produces  a  quadruple  effect. 


ART.    7. 

The  general  laws  of  motion  are  the  three  following, 
viz. 

Law  1.  Every  body  will  continue  in  its  present  state, 
whether  it  be  at  rest  or  moving  uniformly  in  a  right  line, 
except  it  be  compelled  to  change  that  state  by  some  force 
impressed.* 

Law  2.  The  change  of  motion  or  velocity  is  always 
proportional  to  the  square  root  of  the  moving  force  im- 
pressed, and  in  a  right  line  with  that  force,  and  not  as 
the  force  directly. f 

Law  3.  Action  and  re-action  are  always  equal,  and  in 
contrary  directions  to  each  other.  J 

•  By  the  first  law,  a  body  at  rest  inclines  to  continue  so  for  ever,  by  its 
vis  inertia  or  inactive  power,  and  a  body  in  motion  inclines  to  continue  so 
for  ever,  passing  over  equal  distances  in  equal  times,  if  it  meets  with  no 
resistance,  and  will  more  on  in  a  riglit  line.  For  want  of  resistance  the 
planets  and  comets  continue  their  motions  undimmished,  while  moving 
bowls  or  wheels  are  reduced  to  a  state  of  rest  by  the  resistance  of  the 
air,  and  the  friction  of  the  parts  on  which  they  move.  See  Ferguson's 
Lectures  on  Mechanics. 

It  is  this  friction  of  the  parts,  and  resistance  of  the  air,  which  renders 
it  impossible  for  us  to  m;ike  a  perpetual  motion  ;  because  this  friction  and 
resistance  are  to  be  overcome,  and  although  it  may  be  reduced  to  be  very 
small,  yet  man  cannot,  with  ill  his  art,  by  mechanical  combinations,  gain 
as  much  power  as  will  overcome  it.  Philosophers  have  demonstrated  the 
impossibility  of  making  it;  but  I  think  none  ought  to  assert  that  it  will 
never  be  found  ;  for  there  are  many  perpetual  motions  in  the  heavens.  If 
any  man  wo'  Id  spend  his  time  in  this  way,  it  should  be  to  seek  for  a  cre- 
ated power  that  he  might  apply  to  this  purpose,  and  not  to  rreate  one. 

t  This  is  evident,  when  we  consider  that  a  body  must  fall  a  quadruple 
distance  to  obtain  double  velocity,  by  art.  9  ;  and  a  quadruple  head  or 
pressure  of  fluid  produces  a  double  velocity  to  the  spout,  by  art.  46  The 
velocity,  in  both  these  cases,  is  as  the  square  root  of  the  impulse,  and  the 
impulse  as  the  squares  of  the  velochy,  therefore  the  change  of  elec- 
tive motion  or  velocity  will  always  be  as  the  square  root  of  the  impulse 
or  force  impressed,  and  the  force  impressed  as  the  squares  of  the  velocity 
or  effective  motion. 

+  Action  and  re-action  are  equal;  that  is,  if  a  hammer  strikes  an  anvil^ 
the  anvil  will  re-act  against  the  hammer  with  an  equal  force  to  the  action 
of  the  hammer. 


16  MECHANICS.  [Chap.  3. 


CHAPTER  III. 

ART.    8. 
OF  THE  MOMENTUM  OR  FORCE  OF  BODIES  IN  MOTION. 

1.  IF  two  non- elastic  bodies,  A  and  B,  fig.  1  ,each  hav- 
ing the  same  quantity  of  matter,  move  with  equal  velo- 
cities against  each  other,  they  will  destroy  each  other's 
motion,  and  remain  at  rest  after  the  stroke :  because 
their  momentums  will  be  equal ;  that  is,  if  each  has  21bs. 
of  matter  and  10  degrees  of  celerity,  their  instantaneous 
momentums  will  each  be  20. 

But  if  the  bodies  be  perfectly  elastic,  they  will  recede 
from  each  other  with  the  same  velocity  with  which  tl^.ey 
meet ;  because  action  and  re-action  are  equal,  by  the  3d 
general  law  of  motion,  art.  7.* 

2.  If  two  non-elastic  bodies,  A  and  B,  fig.  2,  moving 
in  the  same  direction  with  different  velocities,  impinge 
on  each  other,  they  will  (after  the  stroke)  move  on  to- 
gether with  such  velocity,  as  being  multiplied  into  the 
sum  of  their  weights,  will  produce  the  sum  of  their  in- 
stant momentums  which  they  had  before  the  stroke;  that 
is,  if  each  weigh  lib.  and  A  has  8  and  B  4  dei^rees  of 
celerity,  the  sum  of  their  instant  momentuins  will  be  12, 
then,  after  the  stroke,  their  velocity  will  be  6;  which, 
multiplied  into  their  quantity  of  matter  2,  produces  12, 
the  sum  of  their  instant  momentums.  But  if  they  had 
been  elastic,  then  A  would  have  moved  with  4  and  B 

The  action  of  our  feet  against  the  ground,  and  the  re-action  of  the 
ground  against  our  feet,  are  equal. 

The  action  of  the  hand  to  project  a  stone,  and  the  re-action  of  ihe  stone 
against  the  hand,  are  equal. 

If  a  cannon  weighing  6400  lbs.  gives  a  24  lb.  ball  a  velocity  of  640  feet 
per  second,  the  action  of  the  powder  on  the  ball,  and  its  re  action  ag^nst 
the  cannon,  are  equal ;  and  if  the  cannon  has  liber'y  to  move,  it  will  have 
a  velocity,  which  multiplied  into  its  weight,  will  be  equal  lo  the  velocity 
of  the  ball  multiplied  by  its  weight ;  their  instant  momentums  are  always 
equal      See  Martin's  Philosophy. 

*  This  shews  that  non  elastic  bodies  communicate  onlv  half  their  origi- 
nal force ;  because  the  force  required  to  cause  the  bodies  to  recede  from 
each  other,  is  equal  to  the  force  that  gave  them  velocity  <o  meet ;  and  the 
force  that  caused  the  body  to  recede  with  velocity  10,  is  equal  to  the  force 
that  checked  velocity  10. 


Chap.  3,]  MECHANICS.  17 

with  8  degrees  of  velocity  after  the  stroke,  and  the  sum 
of  their  instant  momentums  would  be  12,  as  before.* 

3.  If  a  non-elastic  body  A,  with  quantity  of  matter  1, 
and  10  degrees  of  \  elocity,  strike  B  at  rest,  of  quantity 
of  matter  1,  they  will  both  move  on  together  with  velocity 
5  ;  but  if  they  be  elastic,  B  flies  off"  with  velocity  10,  and 
A  remains  at  rest,  by  3d  general  law  of  motion,  art.  Y.f 
It  is  universally  true,  that  whatever  instant  momentum  is 
communicated  to  a  body,  is  lost  by  the  body  that  commu- 
nicates it. 

4.  If  die  body  A,  fig.  4,  receive  two  strokes  or  impulses 
at  the  same  time,  in  different  directions,  the  one  sufficient 
to  propel  it  from  A  to  B,  and  the  other  to  propel  it  from 
A  to  D,  in  equal  time,  then  this  compound  force  will  pro- 
pel it  in  the  diagonal  line  A  C,  and  it  will  arrive  at  C  in 
the  same  time  that  it  would  have  arrived  at  B  or  D,  by 
one  impulse  only;  and  the  projectile  force  of  these  strokes 
are  as  the  squares  of  the  sides  of  the  parallelogram,  by 
law  2,  art.  7.| 

•  Because  elastic  bodies  impinginpf,  recede,  after  the  stroke,  with  tiie 
same  velocity  with  which  ihey  id'  et  :  therefore,  a  heavy  body  in  motion, 
impingint^  on  a  lighter  body  at  rest,  will  give  it  a  greater  velocity  than  that 
with  which  it  was  struck;  for  if  tlie  heavy  body  be  not  stopped,  but  move 
forward  after  the  stroke,  with  a  certain  velo  iiy,  that  velocity,  added  to 
the  velocity  before  the  stroke,  will  be  the  velocity  of  the  lighter  body. 

f  This  also  shews  evidently,  that  non-elastic  bodies  communicate  only 
half  their  force.  A  kno^\  ledge  of  this  is  of  greai  use  in  establishing  a 
true  theory  of  water-mills. 

tThis  doctrine  of  the  momentum  of  bodies  in  motion,  and  communica- 
lion  of  motion,  being  as  their  velocities  simply,  was  taught  by  Sir  Isaac 
Newton,  and  has  been  ref-eived  by  his  followers  to  this  d.iy  ;  which  ap- 
pears to  be  true,  where  the  whole  force  is  instantaneoHsly  spent  or  commu- 
nicated :  therefore  I  have  changed  the  term  to  instant  momentum.  I  have 
tried  the  experiment,  by  causing  different  weights  to  strike  eacii  other 
with  diflferent  velocities,  both  on  the  principle  of  pendulums,  and  by  caus- 
ing them  to  move  in  horiznntul  circles;  and,  in  both  cases,  4  lbs  with 
velocity  1,  balanced  2  lbs.  with  velocity  2;  their  momenuims  each  wer.  4: 
so  that  the  theory  appears  to  be  proved  to  be  true.  Yet  I  think  we  have 
reason  to  doubt  its  being  true  in  any  other  sense  ;  because  it  does  not 
agree  with  practice.  All  the  bodies  we  put  in  motion,  to  produce  effects, 
produce  them  in  proportion  to  the  squares  of  their  velocities,  or  nearly,  as 
will  appear  in  the  course  of  this  work.  But  I  fear  I  shall  draw  on  me  the 
ridicule  of  some,  if  I  should  doubt  a  theory  long  establis'ied  ;  but  I  th'hk 
we  should  follow  others  only  in  the  paths  of  truth.  Doubtless  Sir  Isaac 
meant  the  force  to  be  instantly  spent:  and  I  have  understood  that  the 
Dutch  and  Italian  philosophers  have  held  and  taught,  these  100  years  past, 
thi.t  the  momentum  of  bodies  in  motion,  is  as  the  squares  of  their  veloci- 
ties :  and  I  must  confess  it  appears  to  be  really  the  case,  with  respect  to 
the  eflTecls  they  produce  ;  wbicii  is  generally  as  their  quantity  or  weight 

C 


18  MECHANICS.  [Chap.  3. 

5.  If  a  perfect  elastic  body  be  let  fall  4  feet,  to  strike  a 
perfect  elastic  plain,  by  the  laws  of  falling  bodies,  art.  9, 
it  will  strike  the  plain  with  a  velocity  of  16,2  feet  per  se- 
cond, and  rise,  by  its  re-action,  to  the  same  height  from 
whence  it  fell,  in  half  a  second:  if  it  falls  16  feet,  it  will 
strike  with  a  velocity  of  32,4  feet,  and  rise  16  feet  in  one 
second.  Now,  if  we  call  the  rising  of  the  body  the  effect, 
we  shall  find  that  a  double  velocity,  in  this  case,  produces 
a  quadruple  effect  in  double  time.  Hence  it  appears,  that 
a  body  moving  through  a  resisting  medium,  with  a  double 
velocity,  will  continue  in  motion  a  double  time,  and  go  4 
times  the  distance ;  which  will  be  a  quadruple  effect.* 

Of  Non- elasticity  in  impinging  Bodies. 

1.  If  A  and  B,  fig.  3,  be  two  columns  of  matter  in  mo- 
tion, meeting  each  other,  and  equal  in  non-elasticity, 

multiplied  into  the  squares  of  their  velocities.  I  found  it  impossible  to 
reconcile  the  theory  of  the  force  of  bodies  in  motion,  being  as  their  sim- 
ple velocities,  to  the  laws  of  circular  motion,  art.  13,  where  a  double  ve- 
locity produces  a  quadrtiple  central  force ;  of  falling  bodies,  art.  9,  where 
the  velocity  is  as  the  square  root  of  the  impulse  or  distance  fallen,  and 
the  effects  as  the  squares  of  the  velocities;  of  projectiles,  where  a  dou- 
ble velocity  produces  a  quadruple  randum,  art.  12  ;  ot  bodies  descending 
on  inclined  plains,  art.  10,  where  the  velocities  are  as  the  square  roots  of 
the  perpendicular  descents,  and  the  effects  as  the  squares  of  their  veloci- 
ties ;  of  spouting  fluids,  art.  45,  where  their  velocities  are  as  the  square 
roots  of  iheir  perpendicular  heights  or  pressures,  and  their  effects  as  the 
squares  of  their  velocities,  with  equal  q  amities;  of  w.nd  on  mill-sails, 
art.  69,  where  the  effects  are  as  the  cube  of  the  velocity  of  the  wind;  be- 
cause here  the  quantity  is  as  the  velocity,  and  tlie  effect  of  equal  quanti- 
ties being  as  the  squares  of  the  velocity,  amounts  the  effects  to  be  as  the 
cubes. 

But  when  I  discovered  that  a  quadruple  impulse  was  requisite  to  give 
double  velocity,  both  in  falling  bodies  and  spoalmg  fluids,  and,  by  axiom  3, 
the  power  that  produced  a  motion  in  a  body,  and  the  power  that  destroyed 
said  motion,  were  equal,  I  concluded  that  the  effects  produced  by  bodies 
in  motion,  were  as  the  squares  of  their  velocities  ;  and  then  I  found  the 
whole  theory  to  agree  with  practice  Hereafter  I  shall  say,  that  the  ef- 
fective momentum,  or  force  of  bodies  in  motion,  is  as  the  squares  of  their 
velocities. 

•  We  should  pay  no  regard  to  time,  in  calculating  the  effective  force  of 
bodies  in  motion.  Because,  if  1  lb.  of  matter  move  with  1  degree  of  velo- 
city, it  will  produce  a  certain  effect  (before  it  ceases  moving)  in  an  un- 
known time-  Every  other  pound  of  matter,  moving  with  equal  velocity, 
will  produce  an  equal  effect  in  equal  time.  But  if  each  pownd  of  matter 
move  with  double  velocity,  it  will  produce  4  times  the  effect,  but  requires 
a  double  time;  which  difference  in  nme  no  way  affects  the  sum  total  of 
the  effects  oP  the  matter  put  in  motinn  to  move  any  practical  machine. 
Therefore  we  should  totally  leave  time  out  of  this  calculation,  seeing  it 
tends  to  lead  us  into  errors. 


Chap.  3.]  MECHANICS.  19 

quantity,  and  velocity,  they  will  meet  at  the  dotted  line 
e  e,  destroy  each  other's  motion,  and  remain  at  rest,  pro- 
vided none  of  their  parts  separate. 

2.  But  if  A  is  elastic,  and  B  non-elastic,  they  will  meet 
at  e  e,  but  B  will  give  way  by  battering  up,  and  both  will 
move  a  little  further ;  that  is,  half  the  distance  that  B 
shortens. 

3.  But  if  B  is  a  column  of  fluid,  and  when  it  strikes 
A,  flies  oflf  in  a  lateral  perpendicular  direction,  then  what- 
ever is  the  sum  total  of  the  momentums  of  these  particles 
laterally,  has  not  been  communicated  to  A  ;  therefore  A 
will  continue  to  move,  after  the  stroke,  w  ith  that  said  mo- 
mentum. 

4.  But  with  what  proportion  of  the  striking  velocity  the 
fluid,  after  the  stroke,  will  move  in  the  lateral  direction,  I 
do  not  find  determined ;  but  from  small  experiments  I 
have  made  (not  fully  to  be  relied  on)  I  suppose  it  to  be 
more  than  one  half ;  because  water  falling  four  feet,  and 
striking  a  horizontal  plain,  with  16,2  feet  velocity,  will 
cast  some  few  drops  to  the  distance  of  9  feet  (say  10  feet, 
allowing  one  foot  to  be  lost  by  friction,  &c.)  which  we 
must  suppose  take  their  direction  at  an  angle  of  45  de- 
grees, because  it  is  shewn  in  Martin's  Philosophy,  page 
135,  Vol.  I,  that  a  body  projected  at  an  angle  of  45  de- 
grees will  describe  the  greatest  possible  horizontal  ran- 
dum  ;  also,  that  a  body  falling  4  feet,  and  reflected  with 
its  acquired  velocity  16,2  feet,  at  45  degrees,  will  reach  16 
feet  horizontal  randum,  or  4  times  the  distance  of  the  fall. 
Therefore,  by  this,  1-4  of  10  feet,  equal  to  2,5  feet,  is  the 
fall  that  will  produce  the  velocity  that  produced  it,  viz. 
Velocity  12,64  feet  per  second,  about  3-4  of  the  striking 
velocity. 

5.  And  if  the  force  of  striking  fluids  be  as  the  squares 
of  their  velocities,  as  proved  in  ai't.  67,  by  experiment, 
and  demonstrated  by  art.  46  ;  then  the  ratio  of  the  force 
of  this  side  velocity,  12,64  feet  per  second,  is  to  the  force 
of  forward  velocity,  as  160  to  256,  more  than  half  (about 
,6)  of  the  whole  force  is  here  lost  by  non-elasticity. 

6.  This  side  force  cannot  be  applied  to  produce  any 
further  forward  force,  after  it  has  struck  the  first  obstacle; 


29  MECHANICS.  [Chap.  4. 

because  its  action  and  re-action  balance  each  other  after- 
wards :  which  I  demonstrate  by  fig.  27. 

Let  A  be  an  obstacle,  against  which  the  column  of  wa- 
ter G  A,  of  quantity  16  and  velocity  per  second  16, 
strikes  ;  as  it  strikes  A,  suppose  it  to  change  its  direction, 
at  right  angles,  with  3-4  velocity,  and  strike  B  B  ;  then 
change  again,  and  strike  forward  against  C  C,  and  back- 
wards against  D  D  :  then  again  in  the  side  direction  E  E; 
and  again  in  the  forward  and  backward  directions,  all  of 
which  counteract  each  other,  and  balance  exactly. 

Therefore,  if  we  suppose  the  obstacle  A  to  be  the  float 
of  an  undershot  water-wheel,  the  water  can  be  of  no  fur- 
ther service,  in  propelling  it,  after  the  first  impulse,  but 
rather  a  disadvantage  ;  because  the  elasticity  of  the  float 
will  cause  it  to  rebound  in  a  certain  degree,  and  not  keep 
fully  up  with  the  float  it  struck,  but  re-act  back  against 
the  float  following ;  therefore  it  will  be  better  to  let  it  es- 
cape freely  as  soon  as  it  has  fully  made  the  stroke,  but 
not  sooner,  as  it  will  require  a  certain  space  to  act  in, 
which  will  be  in  direct  proportion  to  the  distance  between 
the  floats. 

7.  From  these  considerativons,  we  may  conclude,  thatthe 
greatest  effect  to  be  obtained  from  striking  fluids,  will  not 
amount  to  more  than  half  the  power  that  gives  them  mo- 
tion ;  but  much  less,  if  they  be  not  applied  to  the  best  ad- 
vantage :  and  that  the  force  of  non-elastic  bodies,  strik- 
ing to  produce  effects,  will  be  in  proportion  to  their  non- 
elasticity. 


CHAPTER  IV. 

ART.    9. 
OF  FALLING  BODIES. 

BODIES  descending  freely  by  their  gravity,  in  vacuo, 
or  in  an  unresisting  medium,  are  subject  to  the  following 
laws  : 

1st.  They  are  equably  accelerated.* 

*  It  is  evident,  that  in  every  equal  part  of  time,  the  body  receives  an 
impulst  from  gravity,  that  will  propel  it  an  equal  distance,  and  give  it  an 
equal  additional  vclociiy ;  iherelbre  it  wdl  produce  equal  effects  in  equal 
times,  and  their  velocity  will  be  proportioned  to  the  time. 


Ghap.  4.]  MECHANICS.  21 

2d.  Their  velocity  is  always  in  proportion  to  the  time 
of  their  fall,  and  the  time  is  as  the  square  root  of  the  dis- 
tance fallen.* 

3d.  The  spaces  through  which  they  pass,  are  as  the 
square  of  the  times  or  velocities.!    Therefore, 

4Th.  Their  velocities  are  as  the  square  root  of  the  space 
descended  through  ;%  and  their  force,  to  produce  effects, 
as  their  distances  fallen  directly. 

5th.  The  space  passed  through  the  first  second,  is  veiy 
nearly  16,2  feet,  and  the  velocity  acquired,  at  the  lowest 
point,  is  32,4  feet  per  second. 

6th.  A  body  will  pass  through  twice  the  space,  in  a 
horizontal  direction,  with  the  last  acquired  velocity  of  the 
descending  body,  in  the  same  time  of  its  fall.§ 

7th.  The  total  sum  of  the  effective  impulse  acting  on 
them  to  give  them  velocity,  is  in  direct  proportion  to  the 
space  descended  through,])  and  their  velocity  being  as 
the  square  root  of  the  space  descended  through ;  or,  which 
is  the  same,  as  the  square  root  of  the  total  impulse. 
Therefore, 

8th.  Their  momentums,  or  force  to  produre  effects, 
are  as  the  squares  of  their  velocities,T[  or  directly  as  their 

*  If  llie  velocity,  at  the  end  of  one  second,  be  32,4  feet,  at  the  end  of 
two  seconds  it  will  be  64,8,  at  the  end  of  three  seconus  97,2  feet  per  se- 
cond, and  so  on. 

f  That  is,  as  the  square  of  1  second  is  to  the  space  passed  through  16,2, 
so  is  the  square  of  2  seconds,  which  is  4,  to  64,8  feei,  passed  through  at 
the  end  of  2  seconds,  and  so  on,  for  any  number  of  seconds.  Thtrefore 
the  spaces  passed  through  at  the  end  of  every  second,  wdl  be  as  the 
square  numbers  1,  4,  9,  16,  25,  36,  &c.  and  the  spaces  passed  through, 
in  each  second  separately,  will  be  as  the  odd  numbers  1,  3,  5,  7,  9,  11,  13, 
15,  &c. 

Jf  That  is,  as  the  square  root  of  4,  which  is  2,  is  to  16,2,  the  velocity 
acquired  in  fallinaj  four  feet :  so  is  the  square  root  of  any  other  distance, 
to  the  velocity  acquired,  in  falling  that  distance. 

§That  is,  supp  se  the  body  as  it  arrives  at  the  lowest  point  of  its  fall, 
and  has  acquired  its  greatest  velocity,  was  to  be  turned  in  a  horizontal 
direction,  and  the  velocity  to  continue  uniform,  it  would  pass  over  double 
the  distance,  in  that  direction  ihat  it  had  descended  through  in  the  same 
time. 

II  This  is  evident  from  the  consideration,  that  in  every  equal  part  of  dis- 
tance it  descends  through,  it  receives  an  equal  efllective  impulse  from  gra- 
vity. Therefore  4  times  the  distance,  gives  4  times  the  effective  (but  not 
instant)  impulse. 

1[This  is  evident,  when  we  consider,  that  a  quadruple  distance  or  im- 
pulse, produces  only  double  velocity,  and  by  axiom  3  a  quadruple  resist- 
ance will  be  required,  to  stop  double  velocity  ;  consequently  their  force  is 


22  MECHANICS.  [Chap.  4. 

distances  fell  through ;  and  the  times  expended  in  produ- 
cing the  effects,  are  as  the  square  root  of  the  distance 
fallen  through.* 

9th.  The  resistance  they  meet  with  in  any  given  time, 
in  passing  through  a  resisting  medium,  is  as  their  surfaces, 
and  as  the  cubes  of  their  velocities.f 

as  the  squares  of  their  velocities,  which  brin^^s  them  to  be  directly  as 
their  distances  descended  through  :  and  this  agrees  with  the  second  law 
of  spouting  fluids.     Art.  45. 

*  That  is,  if  a  body  fall  16  feet,  and  strike  a  nonelasiic  body,  such  as 
hot  iron,  soft  lead,  clay,  &c.  it  will  strike  with  velocity  "2,  and  produce  a 
certain  efff  ct  in  a  certain  time.  Again,  if  it  fall  64  feet,  it  w  II  stnke  with 
velocity  64,  and  produce  a  quadruple  effect,  in  a  double  time;  because, 
if  a  perfectly  elastic  body  fall  16  feet  in  one  second  ot  time,  and  strike  a 
perfectly  elastic  plain,  with  velocity  32  fee  ,  it  vviU  rise  16  feel  in  one  se- 
cond of  time.  Again,  if  the  body  fall  two  seconds  of  time,  it  wilt  fall  64 
feet,  and  strike  with  velocity  64,  and  rise  64  feet  in  two  seconds  ot  time. 
Now,  if  we  call  the  rising  of  the  body  the  efiect  of  ihe  striking  velocity 
(which  it  really  is)  then  all  will  appear  clearly.  But  any  thing  here  ad- 
vanced, if  contrary  to  the  opmion  of  many  learned  and  ingenious  authors, 
ought  to  be  doubted,  unless  known  to  agree  with  practice. 

"t"  This  is  evident  when  we  consider, 

1.  That  it  is  a  proportion  of  the  surfaces,  that  meets  the  resistance  ;  and, 

2.  That  a  double  velocity  strikes  a  double  quantity  of  resisting  parti- 
cles in  the  same  time. 

3.  That  a  double  velocity  strikes  each  particle  with  double  the  instant, 
and  four  times  the  effective  force,  by  art.  6. 

Therefore,  the  instant  resistance  is  as  the  squares  of  their  velocities, 
and  will  soon  amount  to  the  whole  force  of  gravity,  and  reduce  the  mo- 
tion to  be  uniform.  This  is  the  reason  why  hail  and  rain  falls  with  such 
moderate  force  ;  whereas  if  it  was  not  for  the  resistance  of  the  air.  they 
would  prove  fatal  to  those  they  tall  upon.  Compare  this  with  the  effect 
of  wind  on  mill  sails,  proved  by  experiment,  to  be  as  'he  c  bes  of  the  ve- 
locity, art  69,  and  with  the  effects  of  spoutin„  fl  ids,  proved  to  be  as  the 
cubes  of  their  velocities,  witb  equal  apertures.  Art.  67,  and  7th  law  of 
spouting  fluids. 

Again,  consider  that  the  solid  content  of  bodies  decreases,  as  the  cubes 
of  their  diameters,  while  their  surfaces  decrease  only  as  the  squaies  of 
their  diameters  ;  consequently  the  smaller  the  body,  the  greater  the  re- 
sistance, in  proportion  to  its  weight:  and  this  is  the  reason  why  heavy  bo- 
dies, reduced  to  dust,  will  float  in  the  air;  as,  likewise,  feathers,  and  ma- 
ny other  bodies  of  great  surface  and  little  matter-  This  seems  to  shew, 
that  air  is,  perhaps,  as  heavy  as  any  other  matter  whatever,  of  an  equal 
degree  of  fineness  or  smallness  of  particles. 

These  are  the  laws  of  falling  bodies  supposing  them  to  fall  m  vacuo,  or 
jn  an  unresisting  medium;  and  without  considering  »hai  gravity  increases, 
as  the  square  of  the  distance  from  the  centre  of  gravity  of  the  attracting 
power  decreases  (4- law  of  gravity,  art.  2;)  because  any  small  distance, 
such  as  comes  in  our  practice,  will  make  no  sensible  difference.  But  as 
they  fall  in  the  air,  which  is  a  medium,  of  great  resistance,  the  instant  re- 
sistance is  as  the  opposing  surfaces  of  the  falling  bidy,  and  as  the  squares 
of  their  velocities,  their  motion  will  greatly  differ  from  these  laws,  m  tail- 
ing great  distances,  or  with  light  bodies  ;  but  in  small  distances,  such  as 
SO  feet  or  less,  and  heavy  bodies,  the  difference  will  be  imperceptible  in 
common  practice. 


Chap.  4.] 


MECHANICS. 


23 


A  TABLE 


MOTION  OF  FALLING  BODIES. 

SUPPOSED  IN  VACUO. 


o 

H 

Ui 

O 

<! 

3' 

us'  O 

5'^i. 

Q 

» 
a 
o 
o 

~  to 
n  K 
n  n 

S    2    85 
r»    "^    O 

If 

o  o 

•m 

«3 

—    an 

M  3  -a 

r  o- 

P-c.o 

o  n 

^^ 

z  ">  " 

n  cr 

n 
p  ? 

?  rt  = 

o 

c 

^% 

S.O 

eg. 

O  V- 

c  ^ 

5"cr 
crp  o 

•ocfi 

5' 

5  =" 

•    a. 

2  3 

1 

81 

^ 

F  5' 

i^a. 

.125 

•25 

4. 

2 

11.4 

.25 

101 

81 

3 

14. 

.5 

405 

16.2 

4 

16.2 

.75 

911 

24  3 

5 

18. 

1 

16-2 

32.4 

6 

19.84 

2 

64  8 

64  8 

7 

21.43 

o 

145  8 

97.2 

8 

22.8 

4 

2592 

1296 

9 

24.3 

5 

305. 

162. 

10 

25.54 

6 

583  2 

194.4 

11 

26.73 

7 

793  8 

226.8 

12 

28. 

8 

1036.8 

259.2 

18 

2916 

9 

1312.2 

2916 

14 

30.2 

10 

1620. 

324. 

15 

31  34 

30 

14580. 

972. 

16 

32.4 

60 

58320. 

1944- 

17 

33.32 

18 

34.34 

19 

35.18 

20 

56.2 

21 

37  11 

36 

48.6 

49 

56  7 

64 

64.8 

100 

81 

144 

97.2 

24  MECHANICS.  [Chap.  4. 

A  SCALE 

OF  THE 

MOTION  OF  FALLING  BODIES.* 


O   (-1 


16. 2  tei  t  is  thi-  space  fullen  throui^h  the  1st  second,  by  law 

5,  which  let  be  eqaal  to 

Which  is  also  the  whole  space  fallen  through  at  the  end  of 
iht-  1st  second,  which  let  be  equal  to         -        -         - 
ot32  4  fee- 1  per  second  is  the  velocity  acquired  by  the  fall, 

io    ditto         - 

.  a 

.'      48  6  feet  is  the  space  fallen  through  the  2d  second,  ditto 
j  3^64  8  feet  do.  at  the  end  of  2  seconds,  ditto 
•j  oo64-8  feet  is  the  velocity  per  second,  acquired  at  the  end  of 
the  2d  second,  ditto  - 

(81.  feet  IS  ihe  space  fallen  through  the  3d  second  of  time,  do- 
1458  feet  ditto  in  3  seconds  of  time,  ditto 


d  ■      97  0  feet  is  the  velecity  acquired  by  the  fall  at  the  end  of  3 
S;-conds,  ditto  ....... 

113  4  iert  IS  the  sp.ce  fallen  through  in  the  4th  second  of 

<  mt,  ditto -         - 

259-2  feet  ditto  in  4  seconds,  ditto      -        .        -        . 


129  6  feet  per  second,  is  the  velocity  acquired  at  the  end  of 
4  seconds,  ditto        ....... 


16 


•  In  this  table,  the  first  column  contains  the  total  space  fallen  through, 
which  is  as  the  squares  of  the  times  or  velocities,  by  law  3  The  second 
column  contains  the  velocity  acquired,  which  is  as  the  square  root  of  the 
dis  arice  fallen,  and  as  the  time  of  the  fall,  by  laws  2  and  4.  The  third 
column  contains  the  space  fallen  through  each  second,  which  is  as  the  odd 
numbers- 


Chap,  5.]  MECHANICS.  25 

This  scale  shews  at  one  view,  all  the  laws  to  be  per- 
formed by  the  falling  body  o,  which  falls  from  o  to  1, 
16,2  feet,  the  first  second,  and  acquires  a  velocity  that 
■would  carry  it  32,4  feet,  from  1  to  a,  the  next  second, 
by  laws  5  and  6  ;  this  velocity  would  also  carry  it  down 
to  b  in  the  same  time,  but  its  gravity,  producing  equal 
effects,  in  equal  times,  will  accelerate  it  so  much  as  to 
take  it  to  3  in  the  same  time,  by  law  L  It  Avill  now  have 
a  velocity  of  64,8  feet  per  second,  that  will  take  it  to  c 
horizontally,  or  down  to  d,  but  gravity  will  help  it  on  to 
5  at  the  same  time.  Its  velocity  will  now  be  97,2  feet, 
which  w'\\\  take  it  horizontally  to  e,  or  down  to  f,  but  gra- 
vity will  help  it  on  to  7 ;  and  its  last  acquired  velocity 
will  be  129,6  feet  per  second  from  7  to  g. 

If  either  of  these  horizontal  velocities  be  continued,  the 
body  will  pass  over  double  the  distance  it  fell,  in  the  same 
time,  by  law  6. 

Again,  if  o  be  perfectly  elastic,  and  falling,  strikes  a 
perfect  elastic  plane,  either  at  1,  3,  5  or  7,  the  effective 
force  of  its  stroke  will  cause  it  to  rise  again  to  o  in  the 
same  space  of  time  it  took  to  fall. 

Which  shews,  that  in  every  equal  part  of  distance,  it 
received  an  equal  effective  impulse  from  gravity,  and  that 
the  total  sum  of  their  effective  impulse  is  as  the  distance 
fallen  directly — and  the  effective  force  of  their  strokes  will 
he  as  the  squares  of  their  velocities,  by  laws  7  and  8. 


CHAPTER  V. 

ART.    10. 

OF  BODIES  DESCENDING  INCLINED  PLANES  AND  CURVED 
SURFACES. 

BODIES  descending  inclined  planes  and  curved  sur- 
faces, are  subject  to  the  following  laws  : 

1.  They  are  equably  accelerated,  because  their  motion 
is  the  effect  of  gravity. 

2.  The  force  of  gravity  propelling  the  body  A,  fig.  5,  to 
descend  an  inclined  plane  A  D,  is  to  the  absolute  gravity 

D 


26  MECHANICS.  [Chap.  6. 

of  the  body,  as  the  height  of  the  plane  A  C  is  to  its  length 
AD. 

3.  The  spaces  descended  through  are  as  the  squares  of 
the  times. 

4.  The  times,  in  which  the  different  planes  A  D,  A  H, 
and  A  I,  or  the  altitude  A  C,  are  passed  over,  are  as  their 
lengths  respectively. 

5.  The  velocities  acquired  in  descending  such  planes, 
in  the  lowest  points  D,  H,  I  or  C,  are  all  equal. 

6.  The  times  and  velocities  of  bodies  descending 
through  planes  alike  inclined  to  the  horizon,  are  as  the 
square  roots  of  their  lengths. 

7.  Their  velocities,  in  all  cases,  are  as  the  square  roots 
of  their  perpendicular  descent. 

From  these  laws  or  properties  of  bodies  descending 
inclined  planes,  are  deduced  the  following  corollaries, 
viz. 

1.  That  the  time,  in  which  a  body  descends  through 
the  diameter  A  C,  or  any  chord  A  a,  A  e,  or  A  i,  are  equal. 
Hence, 

2.  All  the  chords  of  a  circle  are  described  in  equal 
times. 

3.  The  velocity  acquired  in  descending;  through  any 
arch,  or  chord  of  an  arch,  of  a  circle,  as  at  C,  in  the  low- 
est point  C,  is  equal  to  the  velocity  that  would  be  acquir- 
ed in  falling  through  the  perpendicular  height  F  C. 

The  motion  of  pendulums  have  the  same  properties, 
the  rod  or  string  acting  as  the  smooth  curved  surface. 

For  demonstration  of  these  properties,  see  Martin's 
Philosophy,  vol.  i.  page  111 — 117. 


CHAPTER  VI. 

ART.    13. 

OF  THE  MOTION  OF  PROJECTILES. 

A  PROJECTILE  is  a  body  thrown  or  projected  in 
any  direction ;  such  as  a  stone  from  the  hand,  water 
spouting  from  any  vessel,  a  ball  from  a  cannon,  &:c. 
fig.  6. 


Chap,  r.]  MECHANICS.  27 

Every  projectile  is  acted  on  by  two  forces  at  the  same 
time,  viz.  the  Impulse  and  the  Gravity. 

By  the  impulse,  or  projectile  force,  the  body  will  pass 
over  equal  distances,  A  B,  B  C,  &.c.  in  equal  times,  by 
1st  general  law  of  motion,  art.  7,  and  by  gravity,  it  de- 
scends through  the  spaces  AG,  G  H,  &c.  which  are  as 
the  squares  of  the  times,  by  3d  law  of  falling  bodies,  art. 
9.  Therefore,  by  these  forces  compounded,  the  body 
will  describe  the  curve  A  Q,  called  a  parabola ;  and  this 
will  be  the  case  in  all  directions,  except  perpendicular ; 
but  the  curve  will  vary  with  the  elevation,  yet  it  will  still 
be  what  is  called  a  parabola. 

If  the  body  is  projected  at  an  angle  of  45  degrees  ele- 
vation, it  will  be  thrown  to  tlie  greatest  horizontal  distance 
possible ;  and,  if  projected  with  double  velocity,  it  will 
describe  a  quadruple  randum. 

For  a  full  account  and  demonstration,  see  Martin's  Phil, 
vol.  i.  p.  128—135. 


CHAPTER  VII. 

ART.    13. 

OF  CIRCULAR  MOTION  AND  CENTRAL  FORCES. 

IF  a  body  A,  fig.  7,  be  suspended  by  a  string  A  C,  and 
caused  to  move  round  the  centre  C,  that  tendency  which 
it  has  to  fly  from  the  centre,  is  called  the  centrifugal  force ; 
and  the  action  of  the  string  upon  the  body,  which  con- 
stantly solicits  it  towards  the  centre,  and  keeps  it  in  the 
circle  A  M,  is  called  the  centripetal  force.  Speaking  of 
these  two  forces  indefinitely,  they  are  called  centi-al 
forces.* 

The  particular  laws  of  this  species  of  motion,  are, 

•  It  may  be  well  to  observe  here,  that  this  central  force  is  no  real  power, 
but  only  an  effect  of  the  power  that  gives  the  body  the  motion.  Its  inertia 
causes  it  to  recede  from  the  centre,  and  fly  off  in  a  direct  tangent  line, 
With  the  circle  it  moves  in.  Therefore  this  central  force  can  neither  add 
to,  nor  diminish  from,  the  power  of  any  mechanical  or  hydra-jlic  engine, 
unless  it  be  by  friction  and  inertia,  where  water  is  the  moring  power  and 
the  machine  changes  its  direction. 


28  MECHANICS.  [Chap.  7. 

1.  Equal  bodies  describing  equal  circles  in  equal  times» 
have  equal  central  forces. 

2.  Unequal  bodies  describing  equal  circles  in  unequal 
times,  their  central  forces  are  as  their  quantities  of  matter 
multiplied  into  their  velocities. 

3.  Equal  bodies  describing  unequal  circles  in  equal 
times,  their  velocities  and  central  forces  are  as  their  dis- 
tances from  their  centres  of  motion,  or  as  the  radius  of 
their  circles.*" 

4.  Unequal  bodies  describing  unequal  circles  in  equal, 
times,  their  central  forces  are  as  their  quantities  of  mat- 
ter multiplied  into  their  distance  from  the  centre  or  ra- 
dius of  their  circles. 

5.  Equal  bodies  describing  equal  circles  in  unequal 
times,  their  central  forces  are  as  the  squares  of  their 
velocities ;  or,  in  other  words,  a  double  velocity  gene- 
rates a  quadruple  central  force. f     Therefore, 

6.  Unequal  bodies  describing  equal  circles  in  unequal 
times,  their  central  forces  are  as  their  quantities  multi- 
plied into  their  velocities. 

*  This  shews,  that  when  mill-stones  are  of  unequal  diameters,  and  re- 
volve in  equal  times,  the  largest  would  have  the  draught  of  their  furrows 
less,  in  proportion  as  their  central  force  is  more,  which  is  inverse  propor- 
tion ;  also  that  the  draught  of  a  stone  should  vary,  and  be  in  inverse  pro- 
portion to  ilie  distance  from  the  centre.  That  is,  the  greater  the  distance 
the  less  the  draught. 

Hence  we  conclude,  that  if  stones  revolve  in  equal  times,  their  draught 
must  be  equal  next  the  centre  :  that  iF>  so  much  of  the  large  stones,  as  is 
equal  to  the  size  of  the  small  ones,  must  be  of  equal  draught.  But  that 
part  which  is  greater,  must  have  less  draught  in  inverse  proportion,  as  the 
distance  from  the  centre  is  greater,  the  furrows  must  cross  at  so  much  less 
angle;  which  will  be  neax'ly  the  case  (if  their  furrows  lead  to  an  equal 
distance  from  their  centres)  at  any  considerable  distance  from  the  centre  of 
the  stone ;  but  near  the  centre  the  angles  become  greater  than  the  propor- 
tion: if  the  furrows  be  straight,  as  appears  by  the  lines,  g  1>  h  1,  g2,  h  2, 
g  3,  h  3,  in  fig.  1,  pi.  XI.  the  angles  near  the  centre  are  too  great,  whicli 
seems  to  indicate,  that  the  furrows  of  mill-stones  should  not  be  straight, 
but  a  little  curved ;  but  what  this  curve  should  be  is  very  difficult  to  de- 
termine exact!}'  by  theory.  By  theory  it  should  be  such  as  to  cause  the 
angle  of  furrows  crossing,  to  change  in  inverse  proportion  with  the  dis- 
tance from  the  centre,  which  will  require  the  furrows  to  curve  more,  as 
they  approach  the  centre. 

-j-  This  shews  that  mill-stones  of  equal  diameters,  having  their  velocities 
unequal,  should  have  the  draught  of  their  furrows,  as  the  square  roots  of 
their  number  of  revolutions  per  minute-  Thus,  suppose  the  revolutions  of 
one  stone  to  be  81  per  minute,  and  the  mean  draught  of  the  furrows  5 
inches,  and  found  to  be  right ;  the  revolutions  of  the  other  to  be  100  ;  then 
to  find  the  draught,  say.  As  the  square  root  of  81,  which  is  9,  is  to  the  5 
inches  draught ;  so  is  the  square  root  of  100,  which  is  10,  to  4,5  inches, 
the  draught  required  (by  inverse  proportion)  because  the  draught  must 
decrease  as  the  central  force  increases- 


Chap,  r.]  MECHANICS.  29 

7.  Equal  bodies  describing  unequal  circles  widi  equal 
celerities,  dieir  central  forces  are  inversely  as  their  dis- 
tances from  the  centre  of  motion  or  radius  of  the  circles.  *^ 

8.  Equal  bodies  describing  unequal  circles,  having 
their -central  forces  equal;  their  periodical  times  areas 
the  square  roots  of  their  distances. 

9.  Therefore  the  squares  of  the  periodical  times  are 
proportional  to  the  cubes  of  their  distances,  when  neither 
the  periodical  times  nor  the  celerities  are  given.  In  that 
case, 

10.  The  central  forces  are  as  the  squares  of  the  dis- 
tances inversely.! 

*  That  is,  the  greater  the  distance  the  less  the  central  force.  This 
shews  that  niill-stunes  of  different  diameters,  having  their  peripheries  re- 
volving with  equal  velocities,  should  have  the  angle  of  draught,  with  which 
their  furrows  cross  each  other,  in  inverse  proportion  to  their  diameters, 
because  their  central  forces  are  as  tiieir  diameters,  by  inverse  proportion, 
directly:  and  the  angle  of  draught  should  increase,  as  the  central  force 
decreases  ;  and  decrease,  as  it  increases. 

But  here  we  must  consider,  that,  to  give  stones  of  different  diameters 
equal  draughts,  the  distance  of  their  furrows  from  the  centre,  must  be  in 
direct  proportion  to  their  diameters.  Thus,  as  4  feet  diameter  is  to  4 
inches  draught,  so  is  5  feet  diameter  to  5  inciies  draught-  To  make  the 
furrows  of  each  pair  of  stones  cross  each  other  at  equal  angles,  in  all  pro- 
portional distances  from  the  centre,  see  fig  1.  plate  XI.  w  here  g  b,  g  d,  g  f, 
h  a,  h  c,  and  h  e,  shew  the  direction  of  the  furrows  of  the  4,  5,  and  6  feet 
stones,  with  their  proportional  draughts  ;  now  it  is  obvious  that  they  cross 
eacli  other  at  equal  angles,  because  the  respective  lines  are  parallel,  and 
cross  in  each  stone,  near  the  middle  of  the  radius,  which  shews  that  in  all 
proportional  distances,  they  cross  at  equal  angles,  consequently  their 
draughts  are  equal. 

But  the  draught  must  be  further  increased,  with  the  diameter  of  the 
stone,  in  order  to  increase  the  angle  of  draught  in  the  inverse  ratio,  as  the 
central  force  decreases. 

To  do  which,  say :  If  the  4  feet  stone  has  central  force  equal  1,  what 
central  force  will  the  5  feet  stone  have  ?     Answer :  ,8  by  the  7th  law. 

Then  say,  If  central  force  1  requires  5  inches  draught,  for  a  5  feet  stone, 
what  will  central  force  ,8  require  ?  Answer:  6,25  inches  draught.  This 
is,  supposing  the  verge  of  each  stone  to  move  with  equal  velocity.  This 
rule  may  bring  out  the  draught  nearly  true,  provided  there  be  not  much 
difference  between  the  diameter  of  the  stones.  But  it  appears  to  me,  that 
neither  the  angles  with  which  the  furrows  cross,  nor  the  distance  of  the 
point  from  the  centre,  to  which  they  direct,  is  a  true  measure  of  the 
draught. 

f  These  are  the  laws  of  circular  motion  and  central  forces.  For  experi- 
mental demonstrations  of  them,  see  Ferguson's  Lectures  on  Mechanics, 
page  27  to  47- 

I  may  here  observe  that  the  whole  planetary  system  is  governed  by  these 
laws  of  circular  motion  and  central  forces.  Gravity  acting  as  the  string, 
and  is  the  centripetal  force  ;  and  as  the  power  of  gravity  decreases,  as  the 
squ»re  of  the  distance  increases,  by  the  4th  law  of  gravity,  art.  2 ;  and  as 
the  centripetal  and  centrifugal  forces  must  always  be  equal,  in  order  to 
keep  the  body  in  a  circle-  Hence  appears  the  reason  why  the  planets  most 


30  MECHANICS.  [Chap.  8. 

CHAPTER  VIII. 

ART.     14. 

GF  THE  CENTRES  OF  MAGNITUDE,  MOTION,  AND  GRAVITY. 

THE  centre  of  magnitude  is  that  point  which  is  equal- 
ly distant  from  all  the  external  parts  of  a  body. 

2.  The  centre  of  motion  is  that  point  which  remains 
at  rest,  while  all  other  parts  of  the  body  move  round  it. 

3  The  centre  of  gravity  of  bodies,  is  of  great  conse- 
quence to  be  well  understood,  it  being  the  principle  of 
much  mechanical  motion,  and  possesses  the  following 
particular  properties  : 

1.  If  a  body  is  suspended  on  this  point,  as  its  centre  of 
motion,  it  will  remain  at  rest  in  any  position. 

2.  If  a  body  is  suspended  on  any  other  point  than  its 
centre  of  gravity,  it  can  rest  only  in  such  position,  that  a 
right  line  drawn  from  the  centre  of  the  earth  through  the 
centre  of  gravity,  will  intersect  the  point  of  suspension. 

3.  When  this  point  is  supported,  the  whole  body  is 
kept  from  falling. 

4.  When  this  point  is  at  liberty  to  descend,  the  whole 
body  will  fall. 

5.  The  centre  of  gravity  of  all  homogeneal  bodies,  as 
squares,  circles,  spheres,  &c.  is  the  middle  point  in  a  line 
connecting  any  two  opposite  points  or  angles. 

remote  from  the  sun  have  their  motion  so  slow,  while  those  near  him  have 
their  motions  swit't ;  because  their  celerities  must  be  such  as  to  create  a 
centrifugal  force  equal  lo  ihe  attraciion  of  f^ravity. 

I  may  here  observe,  that  modern  philosophers  begin  to  doubt  the  exist- 
ence of  inertia,  as  dtfined  by  Newton,  to  be  different  and  independent 
from  gravity,  but  seem  to  conclude  that  they  are  both  one  thing;  but  when 
we  consider  that  the  whole  force  of  s^ravity  is  exerted  as  centripetal  force, 
to  keep  the  heavenly  bodies  in  a  circle,  it  cannot  be  that  same  power, 
cause,  or  principle,  that  causes  the  bodies  to  continue  their  motion,  unless 
one  cause  can  produce  two  effects  each  equal  to  itself,  contrary  to  axiom  4. 
Again  we  may  consider,  that  gravity  decreases,  as  the  squares  of  the  dis- 
tance of  the  body  from  the  attracting  power  increases,  but  inertia  is  the 
same  every  where;  and  if  we  suppose  the  body  to  be  removed  out  of  the 
sphere  of  attraction  of  gravity,  there  will  be  no  gravity  at  all,  yet  inertia 
will  act  in  its  full  power,  to  continue  the  motion  or  rest  of  a  body,  by  ax- 
iom 1  and  2-  Hence  in  this  light  gravity  and  inertia  appear  to  be  two  very 
difTereni  principles,  and  ought  to  be  distinguished  by  different  names:  but 
here  we  may  dispute  about  words,  for  in  other  lights  they  appear  to  be 
the  very  same  thing. 


Chap.  9.]  MECHANICS.  31 

6.  In  a  triangle,  it  is  in  a  right  line  drawn  from  any 
angle  to  bisect  the  opposite  side,  at  the  distance  of  one 
third  of  its  length  from  the  side  bisected. 

7.  In  a  hollow  cone,  it  is  in  a  right  line  passing  from 
the  apex  to  the  centre  of  the  base,  and  at  the  distance 
of  one  third  of  the  side  from  the  base. 

8.  In  a  solid  cone,  it  is  one  fourth  the  side  from  the 
base,  in  a  line  drawn  from  the  apex  to  the  centre  of  the 
base. 

Hence  the  solution  of  many  curious  phasnothena,  as, 
why  many  bodies  stand  more  firmly  on  their  bases  than 
others ;  and  all  bodies  will  fall,  when  their  centre  of  gra- 
vity falls  without  their  base. 

Hence  appears  the  reason,  why  wheel- carriages,  load- 
ed with  stones,  iron,  or  any  heavy  matter,  will  not  over- 
turn so  easy,  as  when  loaded  with  wood,  hay,  or  any  light 
matter ;  for  when  the  load  is  not  higher  than  a  b,  fig.  12, 
the  centre  of  gravity  will  fall  within  the  centre  of  the  base 
at  c ;  but  if  the  load  is  as  high  as  d,  it  will  then  fall  out- 
side the  base  of  the  wheels  at  e,  consequently  it  will  over- 
turn. From  this  appears  the  error  of  those,  who  hastily 
rise  in  a  coach  or  boat,  when  likely  to  overset,  thereby 
throwing  the  centre  of  gravity  more  out  of  the  base,  and 
increasing  the  danger. 


CHAPTER  IX. 

ART.    15. 

OF  THE  MECHANICAL  POWERS. 

HAVING  now  premised  and  considered  all  that  is 
necessary  for  the  better  understanding  those  machines 
called  m.echanical  powers,  we  come  to  treat  of  them,  and 
they  are  six  in  number,  viz. 

^  The  Lever,  the  Pulley,  the  Wheel  and  Axle,  the  In- 
clined Plane,  the  \\  edge,  and  the  Screw. 


32  MECHANICS.  [Chap.  9. 

They  are  called  Mechanical  Powers,  because  they  in- 
crease our  po^^er  of  raising  or  moving  heavy  bodies  ;  and, 
although  they  are  six  in  number,  they  seem  to  be  redu- 
cible to  one,  viz.  the  Lever,  and  appear  to  be  governed 
by  one  simple  principle,  which  I  shall  call  the  First 
General  Law  of  Mechanical  Powers ;  which  is  this,  viz. 
the  momentums  of  the  power  and  weight  are  always 
equal,  when  the  engine  is  in  equilibrio. 

Momentum,  here  means  the  product  of  the  weight  of 
the  body  multiplied  into  the  distance  it  moves  ;  that  is, 
the  power  multiplisd  into  its  distance  moved,  or  into  its 
distance  from  the  centre  of  motion,  or  into  its  velocity,  is 
equal  to  the  weight  multiplied  into  its  distance  moved,  or 
into  its  distance  from  the  centre  of  motion,  or  into  its 
velocity ;  or,  the  power  multiplied  into  its  perpendicular 
descent,  is  equal  to  the  weight  multiplied  into  its  per- 
pendicular ascent. 

The  Second  General  Lav/  of  Mechanical  Powers,  is, 

The  power  of  the  engine,  and  velocity  of  the  weight 
moved,  are  always  in  the  inverse  proportion  to  each 
other;  that  is,  the  greater  the  velocity  of  the  weight 
moved,  the  less  it  must  be ;  and  the  less  the  velocity, 
the  greater  the  weight  may  be,  and  that  universally  in  all 
cases.     Therefore, 

The  Third  General  Law  is. 

Part  of  the  original  power  is  always  lost  in  overcoming 
friction,  inertia,  &c.  but  no  power  can  be  gained  by  en- 
gines, when  time  is  considered  in  the  calculation. 


In  the  theory  of  this  science,  we  suppose  all  planes  to 
be  perfectly  smooth  and  even,  levers  to  have  no  weight, 
cords  to  be  perfectly  pliable,  and  machines  to  have  no 
friction  :  in  short,  all  imperfections  are  to  be  laid  aside, 
until  the  theory  is  established,  and  then  proper  allowan- 
ces are  to  be  made. 


Chap.  9.]  MECHANICS.  33 


ART.    16. 


Of  the  Lever. 

A  bar  of  iron,  wood,  &c.  one  part  of  which  is  sup- 
ported by  a  prop,  and  all  other  parts  turn  or  move  on  that 
prop,  as  their  centre  of  motion,  is  called  a  lever  :  and  its 
length,  on  each  side  of  the  prop,,  is  called  its  arms ;  the 
velocity  or  motion  of  every  part  of  these  arms  is  directly 
as  its  distance  from  its  centre  of  motion,  by  3d  law  of 
circular  motion. 

The  lever — Observe  the  following  laws : 

1.  The  power  and  weight  are  to  each  other,  as  their 
distances  from  the  centre  of  motion,  or  from  the  prop, 
respectively.* 

2.  The  power  is  to  the  weight,  as  the  distance  the 
weight  moves  is  to  the  distance  the  power  moves,  re- 
spectively, f 

3.  The  power  is  to  the  weight,  as  the  perpendicular 
ascent  of  the  weight  is  to  the  perpendicular  descent  of 
the  power.J 

4.  Their  velocities  are  as  their  distances  from  their 
Gentre  of  motion,  by  3d  law  of  circular  motion. 

These  simple  laws  hold  universally  true  in  all  mecha^ 
nical  powers  or  engines ;  therefore  it  is  easy  (from  these 
simple  principles)  to  compute  the  power  of  any  engine, 
either  simple  or  compound ;  for  it  is  only  to  find  how 
much  swifter  the  power  moves  than  the  weight,  or  how 
much  farther  it  moves  in  the  same  time  ;  and  so  much  is 
the  power,  (and  time  of  producing  it)  increased  by  the 
help  of  the  engine. 

*  That  18,  the  power  P,  fig-.  8.  Plate  I-  which  is  1  multiplied  into  its  dis- 
tance B  C,  from  the  centre  12,  is  equal  to  the  weight  12  multiplied  into  its 
distance  AB  l.each  product  being  12. 

t  That  is,  the  power  multiplied  into  its  distance  moved,  is  equal  to  the 
weight  multiplied  into  its  distance  moved. 

\  That  is,  the  power  multiplied  into  its  perpendicular  descent|  is  equal 
to  the  weight  multiplied  into  its  perpendicular  ascent. 

E 


34.  MECHANICS.  [Chap.  9. 

ART.    17. 

GENERAL  RULES  FOR  COMPUTING  THE  POWER  OF  ANY 
ENGINE. 

1.  Divide  either  the  distance  of  the  power  from  its 
centre  of  motion,  by  the  distance  of  the  weight  from  its 
centre  of  motion.     Or, 

2.  Divide  the  space  passed  through  by  the  power,  by 
the  space  passed  through  by  the  weight.  This  space 
may  be  counted  either  on  the  arch  described,  or  per- 
pendiculars. And  the  quotient  will  shew  how  much  the 
power  is  increased  by  the  help  of  the  engine. 

Then  multiply  the  power  applied  to  the  engine,  by 
that  quotient,  and  the  product  will  be  the  power  of  the 
engine,  whether  simple  or  compound. 

EXAMPLES. 

Let  ABC,  Plate  L  fig.  8,  represent  a  lever ;  then  to 
compute  its  power,  divide  the  distance  of  the  power  P 
from  its  centre  of  motion  B  C  V^,  by  the  distance  of  the 
weight  W,  A  B  1,  and  the  quotient  is  12  :  the  power  is 
increased  12  times  by  the  engine ;  which,  multiply  by 
the  po\ver  applied  1,  produces  12,  the  power  of  the  en- 
gine at  A,  or  the  weight  W,  that  will  balance  P,  and 
hold  the  engine  in  equilibrio.  But  suppose  the  arm  A  B 
to  be  continued  to  E,  then,  to  find  the  power  of  the  en- 
gine, divide  the  distance  B  C  12,  by  B  E  6  ;  and  the 
quotient  is  two  ;  \\hich  multiplied  by  1,  the  power  ap- 
plied, produces  2,  the  power  of  the  engine,  or  weight  w 
to  balance  P.  •        - 

Or  divide  the  perpendicular  descent  of  the  power  C  D 
equal  6,  by  the  perpendicular  ascent  E  F  equal  3  ;  and 
the  quotient  2,  multiplied  by  the  power  P  equal  1,  pro- 
duces 2,  the  power  of  the  engine  at  E. 

Or  divide  the  velocity  of  the  power  P  equal  6,  by  the 
velocity  of  the  weight  w  equal  3  ;  and  the  quotient  2, 
multiplied  by  the  power  1,  produces  2,  the  power  of  the 
engine  at  E.  If  the  power  P  had  been  applied  at  8,  then 
it  would  have  required  to  have  been  1  1-2  to  balance  VV, 
or  w:  because  11-2  timqs  8  is  12,  which  is  the  mo- 
mentum of  both  weights  W  and  w.     If  it  had  been  ap- 


Chap.  9.]  MECHANICS.  35 

plied  at  6,  it  must  have  been  2 ;  if  at  4,  it  must  have 
been  3  ;  and  so  on  for  any  other  distance  from  the  prop 
or  centre  of  motion. 


ART.    18. 

THERE  ARE  FOUR  KINDS  OF  LEVERS. 

1.  The  common  kind,  where  the  prop  is  placed  be- 
tween the  weight  and  power,  but  generally  nearest  the 
weight. 

2.  When  the  prop  is  at  one  end,  the  power  at  the 
other,  and  the  weight  between  them. 

3.  When  the  prop  is  at  one  end,  the  weight  at  the 
other,  and  the  power  applied  between  them. 

4.  The  bended  lever,  which  differs  only  in  form,  but 
not  in  properties,  from  the  others. 

Those  of  the  first  and  second  kind  have  the  same 
properties  and  powers,  and  are  real  mechanical  powers, 
because  they  increase  the  power ;  but  the  third  kind  is 
a  decrease  of  power,  and  only  used  to  increase  velocity, 
as  in  clocks,  watches,  and  mills,  where  the  first  mover  is 
too  slow,  and  the  velocity  increased  by  the  gearing  of  the 
wheels. 

The  machinery  of  the  human  frame  is  composed  of 
the  last  kind  of  lever ;  for  when  we  lift  a  weight  by  the 
hand,  resting  the  elbow  on  any  thing,  the  muscle  that 
exerts  the  force  to  raise  the  weight,  is  fastened  at  about 
one  tenth  of  the  distance  from  the  elbow  to  the  hand, 
and  must  exert  a  force  ten  times  as  great  as  the  weight 
raised ;  therefore,  he  that  can  lift  561bs.  with  his  arm  at 
a  right  angle  at  the  elbow,  exerts  a  force  equal  to  5601bs. 
by  the  muscles  of  his  arm.  Wonderful  is  the  power  of 
the  muscles  in  these  cases.  Here  appears  the  reason, 
why  men  of  low  stature  are  stronger  than  those  of  high, 
in  proportion  to  their  thickness,  as  is  generally  the  case. 


ART.     19. 

COMPOUND  LEVER, 

If  several  levers  are  applied  to  act  one  upon  another, 
as  2  ]   3,  in  fig.  9,  Plate  I.  where  No.  1  is  of  the  first 


36  MECHANICS.  [Chap.  9. 

kind,  No.  2  of  the  second,  and  No.  3  of  the  third.  The 
power  of  these  levers,  united  to  act  on  the  weight  w,  is 
thus  found  by  the  following  rule,  which  will  hold  uni- 
versally true  in  any  number  of  levers  united,  or  wheels 
(which  is  similar  thereto)  acting  upon  one  another. 

RULE. 

1st.  Multiply  the  power  P,  into  the  length  of  all  the 
driving  levers  successively,  and  note  the  product. 

2d.  Then  multiply  all  the  leading  levers  into  one 
another  successively,  and  note  the  product. 

3d.  Divide  the  first  product  by  the  last,  and  the  quo- 
tient will  be  the  M'eight  w,  that  will  hold  the  machine  in 
equilibrio. 

This  rule  is  founded  on  the  first  law  of  the  lever,  art. 
16,  and  on  this  principle,  viz. 

If  the  weight  w,  and  power  P,  are  such,  that  when 
suspended  on  any  compound  machine,  whether  of  levers 
united,  or  of  wheels  and  axles,  they  hold  the  machine  in 
eqi.ilibrio.  Then,  if  the  power  P,  is  multiplied  into  the 
radius  of  all  the  driving  wheels,  or  lengths  of  the  driving 
levers,  and  the  product  noted ;  and  the  weight  w  multi- 
plied into  the  radius  of  all  the  leading  wheels,  or  length 
of  the  leading  levers,  and  the  product  noted ;  these  pro- 
ducts will  be  equal.  If  we  had  taken  the  velocities  or 
circumferences  of  the  wheels,  instead  of  their  radius,  they 
would  have  been  equal  also. 

On  this  principle  is  founded  all  rules  for  calculating 
the  power  and  motion  of  wheels  in  mills,  &c.  See  art, 
20  and  74. 

EXAMPLES. 

Given,  the  power  P  equal  to  4,  on  lever  2,  at  8  distance 
from  the  centre  of  motion.  Required,  with  what  force 
lever  1,  fastened  at  2  from  the  centre  of  motion  of  lever 
2,  must  act,  to  hold  the  lever  2  in  equilibrio.* 

•  In  order  to  abbreviate  the  work,  I  shall  hereafter  use  the  following 
Algebraic  signs,  \\z. 


Chap.  9.]  MECHANICS.  37 

By  the  rule,  4x8  the  length  of  the  long  arm,  is  32,  and 
divided  by  2,  the  length  of  the  short  arm,  quotes  16,  the 
force  required. 

Then  16  on  the  long  arm,  lever  1,  at  6  from  the  cen- 
tre of  motion.  Required,  the  weight  on  the  short  arm, 
at  2,  to  balance  it. 

By  the  rule,  16x6=96,  which  divided  by  2,  the  short 
arm,  quotes  48,  for  the  weight  required. 

Then  48  is  on  the  lever  3,  at  2  from  the  centre.  Re- 
quired, the  weight  at  8  to  balance  it. 

Then  48x2=96,  which  divided  by  8,  the  length  of  the 
long  arm,  quotes  12,  the  weight  required. 

Given,  the  power  P=4,  on  one  end  of  the  combination 
of  levers.  Required,  the  weight  w,  on  the  other  end,  to 
hold  the  whole  in  equilibrio. 

Then  by  the  rule,  •4x8x6x2=384  the  product  of  the 
power  multiplied  into  the  length  of  all  the  driving  levers, 
and  2x2x8=32  the  product  of  all  the  leading  levers, 
and  384  1 32=13  the  weight  w  required. 


ART.    20. 

The  same  rule  holds  good  in  calculating  the  powers  of 
machines,  consisting  of  wheels  whether  simple  or  com- 
pound, by  counting  the  radius  of  the  wheels  as  the  levers  ; 
and  because  the  diameters  and  circumferences  of  circles 
are  proportional ;  we  may  take  the  circumference  instead 
of  the  radius,  and  it  will  be  the  same.  Then  again,  be- 
cause the  number  of  cogs  in  the  wheels  constitute  the 
circle,  we  may  take  the  number  of  cogs  and  rounds  in- 
stead of  the  circle  or  radius,  and  the  result  will  be  the 
same. 

Let  fig.  11,  Plate  II.  represent  a  water-mill  (for  grinding 
grain)  double  geared : 

The  sign  -f-  more,  for  addition. 
—  less,  for  subtraction. 
X  multiplied,  for  multiplication. 
•]•  divided,  for  division. 
=  equal,  for  equality. 
Then,  instead  of  8  more  4  equal  12,  I  shall  write  84-4=12.    Instead  of 
32  less  4 equal  8, 12 — 4=8.  Instead  of  6  multiplied  by  4 equal  24, 6x4=24. 
And  instead  of  24  divided  by  3  equal  8,  24.|.3=8. 


38  MECHANICS.  [Chap.  9. 

Number  8  The  water-wheel, 

4  The  great  cog-wheel, 

2  The  wallower, 

3  The  counter  cog-wheel, 

1  The  trundle, 

2  The  mill  stones, 

And  let  the  above  numbers  also  represent  the  radius 
of  the  wheels  in  feet. 

Now  suppose  there  be  a  power  of  5001b.  on  the  wa- 
ter-wheel, required  what  will  be  the  force  exerted  on  the 
mill- stone,  2  feet  from  the  centre. 

Then  by  the  rule,  500x8x2^1=8000,  and  4x3x2 
=24,  by  which  divide  8000,  and  it  quotes  333,331b.  the 
power  or  force  required,  exerted  on  the  mill- stone  two 
feet  from  its  centre,  which  is  the  mean  circle  of  a  6  feet 
stone. — And  as  the  velocities  are  as  the  distance  from 
the  centre  of  motion,  by  3d  law  of  circular  motion,  art. 
13,  therefore,  to  find  the  velocity  of  the  mean  circle  of 
the  stone  2,  deduce  the  following  rule,  viz. 

1st.  Multiply  the  velocity  of  the  water-wheel  into  the 
radius  or  circumference  of  all  the  driving  wheels,  suc- 
cessively, and  note  the  product. 

2.  Multiply  the  radius  or  circumference  of  all  the 
leading  wheels,  successively,  and  note  the  product ;  di- 
vide the  first  by  the  last  product,  and  the  quotient  will 
be  the  answer. 

But  observe  here,  that  the  driving  wheels  in  this  rule, 
are  the  leading  levers  in  the  last  rule. 

EXAMPLES. 

Suppose  the  velocity  of  the  water-wheel  to  be  12  feet 
per  second  ;  then  by  the  rule  12x4x3x2=288  and  8x2 
Xl=16  by  which  divide  the  first  product  288,  and  it 
quotes  18  feet  per  second,  the  velocity  of  the  stone,  2 
feet  from  its  centre. 


Chap.  9.J  MECHANICS.  .'J9 

ART.   21. 

POWER  DECREASES  AS  MOTION  INCREASES. 

It  may  be  proper  to  observe  here,  that  as  the  velocity 
of  the  stone  is  increased,  the  power  to  move  it  is  decreas- 
ed, and  as  its  velocity  is  decreased,  the  power  on  it  to 
move  it  is  increased,  by  2d  general  law  of  mechanical 
powers.  This  holds  universally  true  in  all  engines  that 
can  possibly  be  contrived  ;  which  is  evident  from  the  1st 
law  of  the  lever,  viz.  the  power  multiplied  into  its  velo- 
city or  distance  moved,  is  equal  to  the  weight  multiplied 
into  its  velocity  or  distance  moved. 

Hence  the  general  rule  to  compute  the  power  of  any 
engine,  simple  or  compound,  art.  17.  If  you  have  the 
movine:  power,  and  its  velocity  or  distance  moved,  given, 
and  the  velocity  or  distance  of  the  weight,  then,  to  find 
the  weight,(\\hich,  in  mills,  is  the  force  to  move  the  stone, 
&c.)  divide  that  product  by  the  velocity  of  the  weight  or 
mill-stone,  Sec.  and  it  quotes  the  weight  or  force  exerted 
on  the  stone  to  move  it:  But  a  certain  quantity  or  pro- 
portion of  this  force  is  lost,  in  order  to  obtain  a  velocity 
to  the  stone  ;  which  is  shewn  in  art.  29.* 


ART.    22, 

NO  POWER  C^AttsTED  BY  ENLARGING  UNDERSHOT  WATER- 

■•      ,  i  WHEELS. 

This  seems  a  proper  time  to  shew  the  absurdity  of 
the  idea  of  increasing  the  power  of  the  mill,  by  enlarging 
the  diarneter  of  the  water-wheel,  on  the  principle  of 
lengthening  the  lever,  or  by  double  gearing  mills  where 
single  gears  will  do ;  because  the  power  can  neither  be 
increased  nor  diminished  by  the  help  of  engines,  while 
-the  velocity  of  the  body  moved  is  to  remain  the  same. 

EXAMPLE. 

Suppose  we  enlarge  the  diameter  of  the  water-wheel 
from  8  to  16  feet  radius,  fig.  11,  Plate  II.  and  leave  the 

*  Philosophers  have  hitherto  attributed  this  loss  of  power  to  fricti0n> 
which  is  owing  to  the  vis  inertia  of  matter. 


40  MECHANICS.  [Chap.  9. 

other  wheels  the  same  ;  then,  to  find  the  velocity  of  the 
stone,  allowing  the  velocity  of  the  periphery  of  the  water- 
wheel  to  be  the  same  ( 12  feet  per  second) ;  by  the  rule 
12x4x3x2=288,  and  16x2x1=32,  by  which  divide 
288,  it  quotes  9  feet  in  a  second,  for  the  velocity  of  the 
stone. 

Then  to  find  the  power  by  the  rule  for  that  purpose, 
i;irt,  20,  500x16x2x1=16000,  and  4x3x2=24,  by 
which  divide  16000,  it  quotes  666,661b.  the  power. 
But  as  velocity  as  well  as  power,  is  necessary  in  mills, 
we  shall  be  obliged,  in  order  to  restore  the  velocity,  to 
enlarge  the  great  cog-wheel  from  4  to  8  radius. 

Then,  to  find  the  velocity,  12x8x3x2=576,  and 
16x2x1=32,  by  which  divide  576,  it  quotes  18,  the 
velocity  as  before. 

Then  to  find  the  power  by  the  rule,  art.  20,  it  will  be 
333,33  as  before. 

Therefore  no  power  can  be  gained,  upon  the  principle 
of  lengthening  the  lever,  by  enlarging  the  water-wheel. 

The  true  advantages  that  large  wheels  have  over  small 
ones,  arises  from  the  width  of  the  buckets  bearing  but  a 
small  proportion  to  the  radius  of  the  wheel ;  because  if 
the  radius  of  the  wheel  be  8  feet,  and  the  width  of  the 
bucket  or  float-board  but  1  foot,  the  float  takes  up  1-8  of 
the  arm,  and  the  water  may  be  said  to  act  fairly  upon  the 
end  of  the  arm,  and  to  advantage.  But  if  the  radius  of 
the  wheel  be  but  2  feet,  and  the  width  of  the  float  I  foot, 
part  of  the  water  will  act  on  the  middle  of  the  arm,  and 
act  to  disadvantage,  as  the  float  takes  up  half  the  arm. 
The  large  wheel  also  serves  the  purpose  of  a  fly-wheel ; 
(art.  30),  it  likewise  keeps  a  more  regular  motion,  and 
casts  off  back  water  better.     See  art.  70. 

But  the  expense  of  these  large  wheels  is  to  be  taken 
into  consideration,  and  then  the  builder  will  find  that 
there  is  a  maximum  size,  (see  art.  44),  or  a  size  that 
will  yield  him  the  greatest  profit. 


Chap.  9.]  MECHANICS.  41 

ART.   S3. 

NO  POWER  GAINED   BY  DOUBLE  GEARING  MILLS,  BUT  SOME 

LOST. 

I  might  also  go  on  to  shew  that  no  power  or  advan- 
tage is  to  be  gained  by  double  gearing  mills,  upon  any 
other  principles  than  the  following,  viz! 

1.  The  motion  necessary  for  the  stone,  can  sometimes 
be  obtained  without  having  the  trundle  too  small,  be- 
cause we  are  obliged  to  have  the  pitch  of  the  cogs  and 
rounds,  and  the  size  of  the  spindle,  large  enough  to  bear 
the  stress  of  the  power.  This  pitch  of  gear,  and  size  of 
spindle,  may  bear  too  great  a  proportion  to  the  radius  of 
the  trundle  (as  does  the  size  of  the  float  to  the  radius  of 
the  water-wheel,  art.  22),  and  may  work  hard.  There- 
fore there  may  be  a  loss  of  power  on  that  account ;  as 
there  can  be  a  loss  but  no  gain,  by  3d  general  law  of  me- 
chanical powers,  art.  15. 

2.  The  mill  may  be  made  more  convenient  for  two 
pair  of  stones  to  one  water-wheel.* 


ART.    S4. 
OP  THE  PULLEY- 

2.  The  pulley  is  a  mechanical  power  well  known. 
One  pulley,  if  it  be  moveable  by  the  weight,  doubles  the 
power,  because  each  rope  sustains  half  the  weight. 

But  if  two  or  more  pulleys  be  joined  together  in  the 
common  way,  then  the  easiest  way  of  compudng  their 
power  is,  to  count  the  number  of  ropes  that  join  to  the 
lovver  or  moveable  block,  and  so  many  times  is  the  pow- 
er increased ;  because  all  these  ropes  have  to  be  shor- 
tened, and  all  run  into  one  rope  (called  the  fall)  to  which 
the  moving  power  is  applied.  If  there  be  4  ropes  the 
power  is  increased  fourfold.f  See  plate  1.  fig.  10. 

*  Many  and  great  have  been  the  losses  sustained  by  mill-builders,  on  ac- 
count of  their  not  properly  understanding-  these  principles.  I  have  often 
met  with  great  high  wheels  built,  where  those  of  half  th-  size  and  expense 
would  do  better  ;  and  double  gears,  where  single  would  do  better,  &c-  &c. 

t  In  this  engine  there  is  ^reat  loss  of  origmal  power,  by  the  great  fric- 

F 


43  MECHANICS.  [Chap.  9. 

ART.   25. 

OF  THE  WHEEL  AND  AXLE. 

3.  The  wheel  and  axle,  fig.  17,  is  a  mechanical  pow- 
er, the  same  as  the  lever  of  the  first  kind  ;  therefore  the 
po\'>  er  is  to  the  weight,  as  the  diameter  of  the  axle  is  to 
the  diameter  of  the  wheel ;  or  the  power  multiplied  into 
the  radius  of  the  wheel  is  equal  to  the  weight  multiplied 
into  the  radius  of  the  axle,*  in  an  equilibrium  of  this 
engine. 


ART.    26. 
OF  THE  INCLllNED  PLANE. 

4.  The  inclined  plane  is  the  fourth  mechanical  power; 
and  in  this  the  power  is  to  the  weight,  as  the  height  of 
the  plane  is  to  its  length.  This  is  of  use  in  rolling  heavy 
bodies,  such  as  barrels,  hogsheads,  &c.  into  wheel  car- 
riages, Sec.  and  for  letting  them  down  again.  See  plate 
I.  fig.  5.  If  the  height  of  the  plane  be  half  its  leni^th, 
then  half  the  force  will  roll  the  body  up  the  plane,  that 
would  lift  it  perpendicularly. 


ART.    27. 
OF  THE  WEDGE. 

5.  The  wedge  is  only  an  inclined  plane.  Whence,  in 
the  common  form  of  it,  the  power  applied  will  be  to  the 
resistance  to  be  overcome,  as  the  thickness  of  the  wedge 
is  to  the  length  thereof.     This  is  a  very  great  mechanical 

tion  of  the  pulleys  and  ropes  in  bending-,  &c.  But  there  is  a  very  great  im- 
provement lately  discovered,  on  the  pully,  which  is  as  follows  :  Make  a 
system  of  puUies  of  such  constmction,  that  when  those  of  the  upper  block 
all  fixed  logt  ther  on  one  pin  will  revolve  in  equal  lime,  and  the  same  in 
the  lower  block;  which  effectually  evades  all  the  friction  of  the  sides  uf  the 
pulleys  and  ropes  passing  through  tlie  blocks.  But  as  it  is  almost  impossi- 
ble to  proportion  tiie  diameters  of  the  pullies  to  the  motion  of  the  ropes 
so  exactly,  it  will  be  best  to  let  them  have  liberty  to  turn  on  the  pin,  so  as 
to  stretch  all  the  ropes  equally- 

*  There  is  but  little  loss  of  original  power  in  this  engine,  because  it  has 
but  little  friction. 


ehap.  91]  MECHANICS.  43 

power,  and  may  be  said  to  excel  all  the  rest ;  because 
with  it  we  can  effect,  what  we  cannot  with  any  other  in 
the  same  time,  and  I  think  may  be  computed  in  the  fol- 
lowing manner. 

If  the  wedge  be  12  inches  long  and  2  inches  thick, 
then  the  power  to  hold  it  in  equilibrio  is  as  1  to  balance 
12  resistance ;  that  is,  12  resistance  pres^ng  on  each 
side  of  the  wedge,*  and  when  struck  with  a  mallet,  the 
whole  force  of  the  gravity  of  the  mallet,  added  to  the 
whole  force  of  the  agent  exerted  in  the  stroke,  is  com- 
municated to  the  wedge  in  the  time  it  continues  to  move : 
and  this  force  to  produce  effect,  is  as  the  square  of  the 
velocity,  with  which  the  mallet  strikes,  multiplied  into 
its  weight :  therefore  the  mallet  should  not  be  too  large, 
(see  art.  44),  because  it  may  be  too  heavy  for  the  work- 
man's strength,  and  will  meet  too  much  resistance  from 
the  air,  so  that  it  will  lose  more  by  lessening  the  velocity, 
than  it  will  gain  by  its  weight.  Suppose  a  mallet  of 
lOlb.  strike  with  5  velocitv,  its  effective  momentum  250  ; 
but  if  it  strike  with  10  velocity,  then  its  effective  mo- 
mentum is  1000.  The  effects  produced  by  the  strokes 
will  be  as  250  to  1000 ;  and  all  the  force  of  each  stroke, 
except  what  may  be  destroyed  by  the  friction  of  the 
wedge,  is  added  in  the  wedge,  until  the  sum  of  these 
forces  amount  to  more  than  the  resistance  of  the  body  to 
be  split,  therefore  it  must  give  way  ;  but  when  the  wedge 
does  not  move,  the  whole  force  is  destroyed  by  the  fric- 
tion. Therefore  the  less  the  inclination  of  the  sides  of 
the  wedge,  the  greater  resistance  we  can  overcome  by  it, 
because  it  will  be  easier  moved  by  the  stroke. 

*  Now,  if  we  consider  that  (he  one  12  acting  on  the  one  side  of  the 
wedge  represents  the  re-action  of  the  ground  on  the  underside  of  the  in- 
clined plane,  we  will  then  plainly  see  thai  the  wedge  and  inclined  plane 
are  both  one  thing;  for  if  this  wedge  be  applied  to  raise  a  weight  of  12,  it 
will  require  2  instead  of  1  to  drive  it  under  the  weight.  But  if  'he  ground 
would  give  way  under  the  wedge  as  easily,  and  move  the  same  distance  thaV 
the  weight  raises,  then  the  weight  would  be  raised  only  half  the  height; 
consequently,  1  would  drive  the  wedge  under  the  weighi,and  this  yielding 
of  the  ground  equal  to  the  raising  of  the  weight,  will  truly  represent  the 
yielding  of  the  cleft  on  each  side  of  the  wedge.  And  'his  is  the  true  prin- 
ciple o<  fhe  wedge,  notwithstanding;  so  inwrh  has  been  said  to  prove  it  to 
be  equal  to  2  inclined  plaries.    See  Ferguson's  Lectures. 


44  MECHANICS.  [Chap.  9. 

ART.  es. 

OF  THE  SCREW. 

6.  The  screw  is  the  last  mentioned  mechanical  power, 
and  is  a  circular  inclined  plane  (which  will  appear  by 
wrapping  a  paper,  cut  in  form  of  an  inclined  plane,  round 
a  cylinder)  and  the  lever  of  the  first  kind  combined  (the 
lever  being  applied  to  force  the  weight  up  in  the  inclined 
plane),  and  is  a  great  mechanical  power ;  its  use  is  both 
for  pressure  and  raising  great  weights.  The  power  ap- 
plied is  to  the  weight  it  will  raise,  as  the  distance  through 
which  the  weight  moves  is  to  the  distance  through 
which  the  power  moves ;  that  is,  as  the  distance  of  the 
threads  of  the  screw  is  to  the  circle  the  power  describes; 
so  is  the  power  to  the  weight  it  will  raise.  If  the  dis- 
tance of  the  thread  be  half  an  inch,  and  the  lever  be  15 
inches  radius  and  the  power  applied  be  101b.  then  the 
power  will  describe  a  circle  of  94  inches,  while  the 
weight  raises  half  an  inch  ;  then,  as  half  an  inch  is  to  94 
inches,  so  is  101b.  to  18881b.  the  weight  the  engine  would 
raise  with  101b.  power.  But  this  is  supposing  the  screw 
to  have  no  friction,  of  which  it  has  a  great  deal. 

Perhaps  an  improvement  might  be  made  on  the  screw, 
for  some  particular  uses,  by  introducing  rollers  to  take  off 
the  friction.     See  art.  33. 


ART.    29. 

We  have  hitherto  considered  the  action  and  effect  of 
these  engines,  as  they  would  answer  to  the  strictness  of 
mathematical  theory,  were  there  no  such  thing  as  fric- 
tion or  rubbing  of  parts  upon  each  other ;  by  which 
means,  philosophers  have  allowed,  that  one-third  of  the 
effect  of  the  machine  is,  at  a  medium,  destroyed :  which 
brings  us  to  treat  of  it  next  in  course.* 

*  But  I  think  it  is  evident,  that  this  loss  of  1-3  of  the  original  power  in 
producing-  effects  by  machines,  arises  fronn  the  vis  inertia  of  the  matter  that 
is  to  be  mo»ed.  For  suppose  the  machine  be  an  elevator,  applied  to  ele- 
vate wheat,  Plate  11.  fig-  17,  art.  34,  it  is  evident,  that  if  we  apply  only  as 
much  poiver  as  will  hold  the  weight  of  the  wheat  in  the  buckets  in  equili- 
brio,  we  will  have  no  motion :  then  in  order  to  oblaiH  a  lively  motion,  we 


Chap.  9.]  MECHANICS.  45 

ART.    80. 

OF  THE  FLY-WHEEL,  AND  ITS  USE. 

Before  I  dismiss  the  subject  of  mechanical  powers,  1 
shall  take  notice  of  the  fly-wheel,  the  use  of  which  is  to 
regulate  the  motion  of  engines,  and  should  be  made  of 
cast  metal,  of  a  circular  form,  that  it  may  not  meet  with 
much  resistance  from  the  air. 

Many  have  taken  this  wheel  for  an  increaser  of  power, 
wheras  it  is,  in  reality,  a  considerable  destroyer  of  it ; 
which  appears  evident,  when  we  consider  that  it  has  no 
motion  of  its  own,  but  receives  all  its  motion  from  the 
first  mover,  and,  as  the  friction  of  the  gudgeons  and  re- 
sistance of  the  air  are  to  be  overcome,  it  cannot  be  done 
without  some  power ;  yet  this  wheel  is  of  great  use  in 
many  cases,  viz. 

1st.  For  regulating  the  power,  where  it  is  irregularly 
applied,  such  as  the  treadle  or  crank  moved  by  foot  or 
hand,  as  spinning-wheels,  turning  lathes,  flax-mills,  or 
where  steam  is  applied,  by  a  crank,  to  produce  a  circular 
motion. 

2d.  Where  the  resistance  is  irregular,  by  jerks,  &c. 
such  as  saw-mills,  forges,  sHtting- mills,  powder-mills, 
&c. 

The  fly -wheel,  by  its  inertia,  regulates  the  motion ; 
because,  if  it  be  very  heavy,  it  will  require  a  great  many 
litde  shocks  or  impulses  of  power  to  give  it  a  considera- 
ble velocity,  and  it  will  require  as  many  equal  shocks  of 
resistance  to  destroy  said  velocity,  by  axiom  3.  art.  1. 

While  a  rolling  or  slitting  mill  is  running  empty,  the 
force  of  the  water  is  employed  in  generating  velocity  to 
the  fly-wheel  [a  heavy  water-wheel  will  have  the  same 
effect],  which  force,  summed  up  in  the  fly,  will  be  suffi- 
cient to  continue  the  motion,  without  much  abatement, 
while  the  sheet  is  running  between  the  rollers ;  whereas, 

will  be  obliged  to  apply  a  further  power,  which  I  expect  we  will  find  will 
be  nearly  1-3  of  the  whole,  art.  41;  and  this  1-3  part  of  the  power  will  be 
continually  emplojed  in  changing  the  state  of  the  wheat  from  rest  to  a 
lively  motion-  Besides,  it  is  shewn  in  art.  31,  that  the  friction  of  most 
machines  is  not  more  than  1-20  part  the  weight  upon  a  plane;  and  by  the 
difference  between  the  diameters  of  the  wheels  and  gudgeons,  is  reduced 
to  1.1000  part  of  the  weight,  or  the  moving  power. 


46  MECHANICS.  [Chap.  10. 

had  the  force  of  the  water  been  lost  while  the  mill  was 
empty,  she  vv^ould  have  slackened  in  motion  too  much 
before  the  sheet  got  through.  This  may  be  the  case 
where  water  is  scarce. 


CHAPTER  X. 

ART.    31. 

OF  FRICTION. 

FROM  what  I  can  gather  from  different  authors,*  and 
by  my  own  experiments,  I  conclude  that  the  doctrine  of 
friction  is  as  follows,  and  we  may  say  it  is  subject  to  the 
following  laws,  viz. 

Laws  of  Friction. 

1.  It  is  neither  increased  nor  decreased  by  increasing 
or  decreasing  the   surfaces  of  contact  of  the   moving 

body.t 

2.  It  is  in  proportion  to  the  weight  and  velocity,  con- 
jointly, of  the  moving  body.  J 

•  Philosophers  treating  of  friction,  seem  to  agree  in  telling  us,  that  If  a 
perfectly  hard  body  of  any  weight  could  be  made  perfectly  smooth  and 
even,  and  laid  on  a  horizontal  plane,  perfectly  hard,  smooth,  and  even,  that 
thi  n  the  least  force  would  move  the  said  weight  in  any  horizontal  direc- 
tion;  and  that  it  is  the  roughness  of  the  best  polished  and  smoothed  bo- 
dies, that  is  the  whole  cause  of  friction ;  because  the  body  in  being  moved^ 
has  first  to  be  raised  over  the  prominent  parts,  which  is  of  the  nature  of  an 
inclined  plane.  They  also  say,  in  treating  of  the  attraction  of  cohesion, 
that  if  two  bodies  of  the  same  kind  of  matter  could  be  made  perfectly 
sm  'oth  and  even,  so  that  the  parts  would  meet  exactly,  they  would  strong- 
ly cohere  or  stick  together  by  a' traction  ;  by  which  it  appears  that  the 
doctrine  of  friction  is  not  yet  well  explained. 

\  They  also  say,  that  it  is  prov(^d  by  experiment,  that  if  a  square  piece 
of  wood  or  brass,  as  F,  Plate  II-  fig-  13,  four  inches  wide,  and  1  inch  thick, 
be  made  smooth,  and  laid  on  a  smooth  plane,  A  B  C  D,  and  the  weight  P 
hung  over  a  pulley,  that  it  will  require  the  weight  P  to  be  nearly  1-3  part 
of  the  weight  of  the  body  F,  to  draw  it  along;  and  that  the  same,  whe- 
ther it  be  on  its  flat  side  or  edge.  This  proves  law  1st,  that  friction  is  not 
increased  by  iftcneasing  the  surface  of  contact. 

\  It  has  also  been  proved  by  experiment,  that  if  we  fix  the  lever  L,  to 
draw  the  weight  F,  making  o  its  centre  of  motion,  and  by  a  cord  make  F 
fiist  to  the  lever  at  the  point  1,  and  hang  the  weight  Q  at  the  end  of  the 
lever  over  a  pulley,  and  make  Q  just  sufficient  to  move  F,  Q  wdl  then  be 
found  to  be  1-7  of  P.  because  it  will  have  to  move  F  but  1  7  of  the  distance. 
Thfn  move  the  cord  from  1  to  2,  and  we  find  the  weight  Q  must  now  be 
doubled  equal  to  2-7  of  P  to  moye  F ;  (the  reason  is  evident  from  the  laws 


Chap.  10.]  MECHANICS.  47 

3.  This  proportion  decreases  as  the  weight  and  velo- 
city increases,  but  by  what  ratio  is  not  determined.* 

of  the  lever)  because  F  is  double  the  distance  from  the  centre  of  motion 
that  it  was  at  1,  and  \\  will  have  to  move  double  the  distance  if  the  lever, 
or  power  Q,  move  the  same  distance.  This  shews  that  friction  is  as  the  dis- 
tance from  the  centre  ot  motion;  that  isi  it  is  as  the  diameter  of  the  gud- 
geons, double  diameter,  double  friction  ;  therefore  ^{udgeons  ought  to  be 
as  small  as  possible,  so  as  to  be  sufficiently  strong  to  endure  the  stress  of  the 
weight. 

*  They  have  also  proved  by  experiment,  that  if  F  be  a  brass  plate  of  6 
ounces,  and  A  B  C  D  a  brass  plute,  both  well  polished  and  oiled, » hen  it  will 
require  the  weight  P  lo  be  nearly  2  ounces  to  move  F.  But  if  F  be  loaded 
with  6,  8,  or  10  lb.  then  a  sixth  part  of  that  weight  will  be  sufficient  to  draw 
it  along.  This  proves  that  the  ratio  of  the  friction  to  the  weight  decreases, 
as  the  weight  increases  •  the  reason  of  which  decrease  of  proportion  I  take 
to  be  as  follows,  viz.  Great  part  of  the  friction  arises  from  the  cohesion  of 
the  parts,  even  the  grease  put  on  to  destroy  the  cohesion,  has  a  cohesion  of 
its  own  ;  and  this  cohesion  of  pans  or  of  the  grease,  will  not  increase  with 
the  weight  or  velocity.  Again,  if  we  allow  the  friction  to  be  occasioned  by 
the  weight  of  the  body  having  to  be  raised  over  the  prominent  parts  of  the 
rubbing  surface,  it  is  evident,  that  when  it  is  raised  by  being  started,  that 
it  has  not  to  be  raised  again  ;  therefore  the  greater  the  velocity,  the  less 
proportion  will  this  resistance  (occasioned  by  the  raising  of  the  body)  bear 
to  the  velocity. 

I  have  made  an  experiment  similar  to  that  of  Plate  11-  fig.  13,  with  a 
flat -sided  glass  bottle,  on  a  smooth  poplar  plank,  oiled  ;  also  on  a  well  po- 
lished steel  plate  oiled,  and  when  loaded  with  10  lb.  it  was  drawn  by  1  lb. 
and  when  loaded  with  22  lb.  it  was  drawn  by  21b.  and  when  loaded  with 
601b.  it  was  drawn  by  4  1-2  lbs.  which  is  about  1  13  part :  and  the  motion 
was  greatly  accelerated,  which  gives  reason  to  conclude,  that  less  weight 
would  have  continued  the  motion  when  once  begun. 

We  may  reasonably  suppose,  that  the  gudgeons  of  mills,  &c.  well  polish- 
ed, running  on  good  stones  or  brass  boxes,  &c.  and  well  oiled,  have  as  l.ttle 
friction  as  the  bottle  and  plank  ;  and  as  we  find  that  the  proportion  of  fric- 
tion decreases  as  the  weight  increases,  we  may  suppose  that  in  great 
weights  it  will  not  amount  to  more  than  1  20  part  of  the  weight,  supposing 
the  gudgeons  to  be  the  full  size  or  diameter  of  the  wheels,  for  so  they 
must  be  in  order  to  be  on  the  same  principles  of  planes  rubbing  together. 
Upon  these  principles  I  compute  the  friction  of  the  gudgeons  of  a  well 
hung  water-wheel,  as  follows  :  viz.  As  the  diameter  of  the  wheel  is  to  the 
diameter  of  the  gudgeons,  so  is  1  20  part  of  the  weight  of  the  wheel,  to 
the  weight  that  will  balance  the  friction. 

EXAMPLE, 

Suppose  a  wheel  15  feet  diameter,  with  gudgeons  3  inches  diameter,  and 
weighing  40001b.  by  supposition  ;  then,  say  as  15  feet  is  to  3  inches,  so  is 
400  I  20  to  3,31b.  the  weight  on  the  periphery  of  the  wheel  that  will  ba- 
lance the  friction  of  4000  lb.:  which  is  less  than  1-1000  part  of  the  weight; 
but  note  'hat  for  the  same  reasons,  that  friction  does  not  increase  with  the 
velocity  m  direct  proportion,  neither  will  it  decrease  in  direct  proportion 
with  the  velocity  of  the  rubbing  surface  of  the  gudgeon:  hence  we  must 
conclude  again  that  the  friction  is  more  than  l-lOOO  part.  By  which  it  ap- 
pears, that  the  friction  of  the  gudgeons,  well  set  on  good  stones  or  brass 
boxes,  is  not  in  mills  worthy  the  expense  of  evading.  It  bears  but  a  small 
proportion  to  the  friction  or  resistance  of 'he  air,  especially  where  the  VS' 
locity  is  great.    See  art.  9,  and  9th  kw  of  falling  bodies. 


48  MECHANICS.  [Chap.  10, 

4.  It  is  greatly  varied  by  the  smoothness  or  roughness, 
hardness  or  softness,  of  the  surfaces  of  contact  of  the 
moving  bodies. 

5.  A  body  without  motion  has  no  friction  ;  therefore, 
the  less  the  motion,  the  less  the  friction. 


ART.   3S. 


OF  REDUCING  FRICTION. 


To  reduce  friction,  we  must,  by  mechanical  contriv- 
ances, reduce  the  motion  of  the  rubbing  parts  as  much 
as  possible ;  which  is  done,  either  by  making  the  gud- 
geons small  and  the  diameter  of  wheels  large,  or  by  fix- 
ing the  gudgeons  to  run  on  friction-wheels.  Tlius,  let 
A,  Plate  II.  fig  14,  represent  the  gudgeon  of  a  wheel 
set  to  run  on  the  verge  of  two  wheels  of  cast  metal  pas- 
sing each  other  a  little,  and  the  gudgeon  laving  between 
them.  It  is  evident,  that  as  A  turns,  it  will  turn  both 
friction-wheels ;  and,  if  the  diameter  of  gudgeon  A  is  2 
inches,  and  that  of  the  wheels  12,  then  the  wheels  will 
turn  once  while  A  turns  6  times,  so  that  the  velocity  of 
the  gudgeons  C  C  of  the  wheels,  is  to  the  velocity  of  the 
gudgeon  A,  as  1  is  to  6,  supposing  them  to  be  equal  in 
size ;  but  as  there  are  4  of  them  to  bear  A,  they  may  be 
but  half  the  diameter,  and  then  their  velocity  will  be  to 
that  of  A,  as  1  is  to  12 ;  or  A  might  be  set  on  one 
wheel,  as  at  B,  with  supporters  to  keep  it  on ;  and,  if 
friction-wheels  are  added  to  friction-wheels,  the  friction 
may  be  reduced  to  almost  nothing  by  that  means. 


ART.   33. 
LATE  INVENTION  TO  REDUCE  FRICTION. 

Wheel-carriages,  pullies,  and  such  wheels  as  have 
large  axles  in  proportion  to  their  diameters,  have  much 
friction.  There  has  been  a  late  discovery  in  England,  of 
applying  the  principle  of  the  roller  to  them ;  which  may 
be  so  done  as  almost  totallv  to  destrov  the  friction. 


Ghap.  10.]  MECHANICS.  49 

The  easiest  method  possible,  of  moving  heavy  bodies 
horizontally,  is  the  roller. 

Let  A  B,  Plate  11.  fig.  15,  represent  a  body  of  100  tons 
weight  (with  the  under  side  perfectly  smooth  and  even) 
set  on  two  rollers,  perfectly  hard,  smooth  and  round,  roll- 
ing on  the  horizontal  plane  C  D,  perfectly  hard,  smooth, 
and  even  ;  it  is  evident  that  this  body  is  supported  by 
two  lines  perfectly  perpendicular,  and,  if  globes  were 
used  instead  of  rollers,  the  least  force  would  move  it  in 
any  horizontal  direction ;  even  a  spider's  web  would  be 
sufficient,  giving  it  time  to  overcome  the  vis  inertia  of 
the  body  :  But  as  perfect  hardness,  smoothness,  &c.  are 
not  attainable,  a  litde  friction  will  still  remain. 

This  principle  is,  or  may  be,  applied  to  wheel- car- 
riages, in  the  following  manner  : 

Let  the  outside  ring  BCD,  Plate  IL  fig  16,  represent 
the  box  of  a  carriage- wheel,  the  inside  circle  A  the  axle, 
the  circles  a  a  a  a  a  a  the  rollers  round  the  axle  between 
it  and  the  box,  and  the  inner  ring  a  thin  plate  for  the 
pivots  of  the  rollers  to  run  in,  to  keep  them  at  a  proper 
distance  from  each  other.  When  the  wheel  turns,  the 
rollers  pass  round  on  the  axle,  and  on  the  inside  of  the 
box,  and  we  may  say  without  friction,  because  there  is 
no  rubbing  of  the  parts  past  one  another.* 

*  To  explain  this,  let  us  suppose  the  rollers  a  a  a  a  a  a  to  have  cogs,  and 
the  shaft  A,  and  box  to  have  cogs  also,  the  rollers  gearing  into  the  shaft 
and  into  the  inside  of  the  box.  Now  it  is  evident,  ihat  if  the  box  will  turn 
round  the  axle,  it  must  be  without  any  sliding  of  parts  ;  (and  in  fact,  the 
prominent  parts  of  the  rollers,  axle  and  box,  will  act  as  cogs)  then,  if  the 
rollers  and  axle  be  all  of  one  diameter,  they  will  have  an  eq  lal  number  of 
cogs;  and  as  the  diameter  of  the  box  wdl  be  3  times  the  diameter  of  the 
rollers,  it  will  have  3  times  as  many  cogs.  Now  it  is  evident,  that  the  axle 
must  turn  1  1-3  times  round,  before  the  same  cogs  of  the  rollers  and  shaft 
will  meet,  that  were  together  when  it  started;  because,  in  that  time  the 
rollers  will  have  moved  over  1-3  of  the  box:  therefore  the  axle  mus^  turn 
3  3-3  times  equal  to  4  times  round,  by  the  time  the  box  is  once  measured 
by  the  rollers.  Then  suppose  we  hold  the  axle  at  rest,  and  turn  the  box 
round  like  a  carriage  wheel;  then,  while  the  box  turns  1  1-3  times  round 
the  axle,  it  will  cause  the  rollers  to  move  once  round ;  and  while  the  box 
or  wheel  turns  round  the  axle  4  times,  the  rollers  vvill  run  round  it  three 
times.  For  suppose  we  divide  the  box  into  3  parts,  B  C  and  D,  then  begin- 
ning to  turn  the  box  from  B  to  D,  it  is  evident,  that  while  the  roller  a  b 
measures  once  round  the  axle  and  returns  to  the  same  place,  it  wdl  .ilso 
measare  the  box  from  B  to  C,  and  C  will  have  taken  ihe  place  of  B,  and 
the  next  revolution  of  the  roller  D  will  take  the  place  of  C,  and  the  third 
revolution  B  returns  to  where  it  was  at  first,  and  the  box  has  made  4  revo- 

G 


50  I^ECHANICS.  [Chap,  ll- 


CHAPTER.  XL 


ART.    34. 
OF  MAXIMUMS,  OR  THE  GREATEST  EFFECTS  OF  ANY  MACHINE. 

THE  effect  of  a  machine,  is  the  distance  which  it 
moves,  or  the  velocity  with  which  it  moves  any  body  to 
which  it  is  applied  to  give  motion,  in  a  gi^en  time;  and 
the  weight  of  the  body  multiplied  into  its  distance  mov- 
ed, or  into  its  velocity,  shews  he  effect. 

The  theory  published  by  philosophers,  and  received 
and  taught  as  true,  for  several  centuries  past,  is,  that  any 
machine  \vill  work  with  its  greatest  perfection  when  it 
is  charged  with  just  4-9  of  the  power  that  would  hold  it 
in  equilibrio,  and  then  its  velocity  will  be  just  1-3  of  the 
greatest  velocity  of  the  moving  power. 

To  explain  this,  they  suppose  the  water-wheel,  Plate 
n.  fig.  17,  to  be  of  the  undershot  kind,  16  feet  diameter, 
turned  by  water  issuing  from  under  a  4  feet  head,  with  a 
gate  1  foot  wide,  1  foot  high  drawn  ;  then  the  force  will 
be  250lbs.  because  that  is  the  weight  of  the  column  of 
water  above  the  gate,  and  its  velocity  will  be  16,2  feet 
per  second,  as  shall  be  shewn  under  the  head  of  Hy- 
draulics ;  then  the  wheel  will  be  moved  by  a  power  of 
2501bs.  and  if  let  run  empty,  will  move  with  a  velocity 
of  16  feet  per  second  :  but  if  we  hang  the  weight  W  to 
the  axle  (of  2  feet  diameter)  with  a  rope,  and  continue 
to  add  to  it  until  it  stops  the  wheel,  and  holds  it  in  equi- 
librio, the  weisrht  will  be  found  to  be  2000lbs.  by  the 
rule,  art.  19  ;  and  then  the  effect  of  the  machine  is  no- . 
thing,  because  the  velocity  is  nothing :  But  as  we  de- 
crease the  weight  W,  the  wheel  begins  to  move,  and 
its  velocity  increases  accordingly  ;  and  then  the  product 
of  the  weight  multiplied  into  its  velocity,  will  increase 
until  the  v/eight  is  decreased  to  4-9   of  2000=888,7, 

lotions,  while  the  rollers  have  made  3  round  the  axle,  and  without  any  slid- 
ing of  pans,  therefore  without  friction.  I  might  goon  to  shew,  th.t  if  Ihe 
axle  be  much  larger  than  the  rollers,  they  will  also  work  without  sliding. 


^hap.  11.]  MECHANICS.  51 

which  multiplied  into  its  distance  moved  or  velocity, 
will  produce  the  greatest  effect,  and  the  velocity  of  the 
wheel  then  be  1-3  of  16  feet,  or  5,33  feet  per  second. 
So  say  those  who  ha^'e  treated  of  it. 

This  will  appear  plainer  to  a  young  learner,  if  he  will 
conceive  this  wheel  to  be  applied  to  work  an  elevator,  as 
E,  Plate  II.  fig.  17,  to  hoist  wheat,  and  suppose  that  the 
buckets,  when  all  full,  contain  9  pecks,  and  will  hold  the 
wheel  in  equilibrio,  it  is  evident  it  will  then  hoist  none, 
because  it  has  no  motion  ;  then,  in  order  to  obtain  mo- 
tion, we  must  lessen  the  quantity  in  the  buckets,  when 
the  wheel  will  begin  to  move,  and  hoist  faster  and  faster 
until  the  quantity  is  decreased  to  4-9,  or  4  pecks,  and 
then,  by  the  theory,  the  velocity  of  the  machine  will  be 
1-3  of  the  greatest  velocity,  when  it  will  hoist  the  great- 
est quantity  possible  in  a  given  time  :  for  if  we  lessen 
the  quantity  in  the  buckets  below  4  pecks,  the  quantity 
hoisted  in  any  given  time  will  be  lessened. 

This  is  the  theory  established,  for  demonstration  of 
which,  see  Martin's  Philosophy,  vol.  i.  p.  185 — 187. 


ART.   35. 

OLD  THEORY  INVESTIGATED. 

In  order  to  investigate  this  theory,  and  the  better  to 
understand  what  has  been  said,  let  us  consider  as  follows, 
viz. 

1.  That  the  velocity  of  spouting  water,  under  4  feet 
head,  is  16  feet  per  second,  nearly. 

2.  The  section  or  area  of  the  gate  drawn,  in  feet, 
multiplied  by  the  height  of  the  head  in  feet,  gives  the 
cubic  feet  in  the  whole  column,  which  multiplied  by  62,5 
(the  weight  of  a  cubic  foot  of  water)  gives  the  weight 
or  force  of  the  whole  column  pressing  on  the  wheel 

3.  That  the  radius  of  the  wheel,  multiplied  by  the 
force,  and  that  product  divided  by  the  radius  of  the  axle, 
gives  the  weight  that  will  hold  the  wheel  in  equilibrio. 

4.  That  the  absolute  velocity  of  the  wheel,  subtracted 
from  the  absolute  velocity  of  the  water,  leaves  the  rela- 


52  MECHANICS.  [Chap.  11. 

tive  velocity  with  which  the  water  strikes  the  wheel  in 
motion. 

5.  That  as  the  radius  of  the  wheel  is  to  the  radius  of 
the  axle,  so  is  the  velocity  of  the  wheel  to  the  velocity 
of  the  weight  hoisted  on  the  axle. 

6.  That  the  effects  of  spouting  fluids  are  as  the  squares 
of  their  velocities  (see  art.  45,  law  6),  but  the  instant 
force  of  striking  fluids  are  as  their  velocities  simply. 
See  art.  8. 

7.  That  the  weight  hoisted,  multiplied  into  its  per- 
pendicular ascent,  gives  the  effect. 

8.  That  the  weight  of  water  expended,  multiplied  into 
its  perpendicular  descent,  gives  the  power  used  per 
second. 

On  these  principles  I  have  calculated  the  following 
scale ;  first  supposing  the  force  of  striking  fluids  to  be 
as  the  square  of  their  striking  or  relative  velocity,  which 
brings  out  the  maximum  agreeably  to  the  old  theory, 
viz. 

When  the  load  at  equilibrio,  is  2000,  then  the  maxi- 
mum load  is  §88,7=4-9  of  2000,  when  the  effect  is  at 
its  greatest,  viz.  591,98,  as  appears  in  the  6th  column, 
.  and  then  the  velocity  of  the  wheel  is  5,333  feet  per  se- 
cond, equal  to  1-3  of  16,  the  velocity  of  the  water,  as 
appears  in  the  5th  line  of  the  scale :  but  as  there  is  an 
evident  error  in  the  first  principle  of  this  theory,  by 
counting  the  instant  force  of  the  water  on  the  wheel  to 
be  as  the  square  of  its  striking  velocity,  therefore  it  can- 
not be  true.     See  art.  41. 

I  then  calculate  upon  this  principle,  viz.  That  the 
instant  force  of  striking  fluids  is  as  their  velocity  simply, 
then  the  load  that  the  machine  will  carry,  with  its  dif- 
ferent velocities,  will  be  as  the  velocity  simply,  as  ap- 
pears in  the  7th  column,  and  the  load,  at  a  maxim,  is 
1000lb.=|  of  2000,  the  load  at  equilibrio,  when  the  ve- 
locity of  the  wheel  is  8  feet=|  of  16  the  velocity  of  the 
water  per  second  ;  and  then  the  effect  is  at  its  greatest, 
as  shewn  in  the  8th  column,  viz.  1000,  as  appears  in  the 
4th  line  of  the  scale. 

This  I  call  the  new  theory,  (because  I  found  that 
William  Waring  had  also,  about  the  same  time,  esta- 


Chap.  11.]  MECHANICS.  33 

blished  it,  see  art.  38)  viz.  That  when  any  machine  is 
charged  with  just  1-2  of  the  load  that  will  hold  it  in 
equilibrio,  its  velocity  will  be  just  1-2  of  the  natural  ve- 
locity of  the  moving  power,  and  then  its  effect  will  be  at 
a  maximum,  or  greatest  possible. 

This  appears  to  be  the  way  by  which  this  great  error 
has  been  so  long  overlooked  by  philosophers,  and  which 
has  rendered  the  theory  of  no  use  in  practice,  but  led 
many  into  expensive  errors,  thereby  bringing  great  dis- 
credit upon  philosophy. 

For  demonstrations  of  the  old  theory,  see  Martin's 
Phil.  vol.  i.  p.  185—187. 


S4 


MECHANICS. 


[Chap.  11. 


s; 

s 

H 

J3 


I 


Ritioof  the  power  and  ef 
feet  at  a  niaximum,  the 

-a  ^ 

6  &  .         b:  6  J 

power  being  4000  in  each 

e  =  o^    -^  e^ 

case. 

^.S^ls      -^"3 

s     ;:  2§ 

,; 

oN-ot^aoo^  oio 

Effect,  by  new  theory. 

i«.0>OOl0000I^C0 

Weight  hoisted,  according 

« 

to  new  theory. 

T-4   '^  1-<   p4   l-l    .-•   C4 

■ 

00 
in          o>  ?>  (O  lo  h. 

Effect,  by  the  old  theory. 

<u 

isT-^  o  «^  -T  o  «'  cT 

OOO'OOCOO^OiOQO 

.^  CO  <D  •-  to  lo  »r)    ■> 

Weight   hoisted,  according 

in 

to  the  old  theory. 

J3 

CQOOOOOOO-^tNCOO 
-H  rt  CN 

Velocity  of  the  weight  as- 

OJ 

«3  ifl 
«0         «0  'O  (N         "i^ 

cending. 

VJ  «N        I^  VO  <0^  •O  (N  O 

Velocity  with  whicti  the  wa 

ter  strikes  the   wheel  in 

*^ 

motion,  or  relative  velo- 

'.i 

0'^<00000'-<C^'?<0 

city. 

Velocity  of  the   wheel   per 

^ 

o 

n 

second,  by  supposition 

.u 

<ONO00<o>rriOT}<irNO 

00,-l      r1      ^'O      ■<=>      O 

^  2  »o    o 

.i> 

r»A^         ,->A.*«>r^A^ 

CO         S 

4*           O"        1 

ius  of  the  wheel 
ins  of  the  axle 

ion  of  the  gate  in  square  feet 

j;hi  of  the  head  of  water 

jcity  of  the  water  per  second  - 

ght  of  the  column  of  water  pr 

g  on  the  wheel 

weight  that  holds  the  wheel  in  e 

jrio 

■TJ  "o    o    — ::  jj  c  4)  .- 

f  Chap.  11,  MECHANICS.  BS 

ART.  36. 

NEW  THEORY  DOUBTED. 

But  although  that  I  know  the  velocity  of  the  wheel, 
by  this  neu  theor}',  is  much  nearer  practice  than  the  old, 
(though  rather  slow)  yet  I  am  led  to  doubt  the  theory, 
for  the  following  reasons,  viz. 

When  I  consider  that  there  are  16  cubic  feet  of  water, 
equal  lOOOlbs.  expended  in  a  second,  which  multiplied 
by  its  perpendicular  descent,  4  feet,  produces  the  power 
4(;00.  The  ratio  of  the  power  and  effect  by  the  old 
theory  is  as  10  to  1,47,  and  by  the  new  as  4  to  1  ;  as 
appears  in  the  9th  column  of  the  scale ;  which  is  a  proof 
that  the  old  theory  is  a  great  error,  and  sufficient  cause  of 
doubt  that  there  is  yet  some  error  in  the  new.  And  as 
the  subject  is  of  the  greatest  consequence  in  practical 
mechanics,  therefore  I  proceed  to  endeavour  to  dis- 
cover a  true  theory,  and  will  shew  my  work,  in  order 
that  if  1  establish  a  theory,  it  maybe  the  easier  understood, 
if  right,  or  detected,  if  wrong. 

Attempts  made  to  discover  a  new  Theory. 

In  the  search,  I  constructed  fig.  18,  pi.  II.  which  re- 
presents a  simple  wheel  with  a  rope  passing  over  it  and 
the  weight  P,  of  lOOlbs.  at  one  end  to  act  by  its  gravity, 
as  a  power  to  produce  effects,  by  hoisting  the  weight  w 
at  the  other  end. 

This  seems  to  be  on  the  principles  of  the  lever,  and 
overshot  wheel ;  but  with  this  exception,  that  the  quan- 
tity of  descending  matter,  acting  as  power,  will  still  be 
the  same,  although  the  velocity  will  be  accelerated, 
whereas  in  overshot  wheels,  the  power  on  the  wheel  is 
inversely,  as  die  velocity  of  the  wheel. 

Here  we  must  consider, 

1.  The  perpendicular  descent  of  power  P,  per  se- 
cond, multiplied  into  its  weight,  shews  the  power. 

2.  That  the  weight  w  when  multiplied  into  its  per- 
pendicular ascent  gives  the  effect. 

3.  That  the  natural  velocity  of  the  falling  body  P,  is 
16  feet  the  first  second,  and  the  distance  it  has  to  fall 
16  feet. 


56  MECHANICS.  [Chap.  11. 

4.  That  we  do  suppose  that  the  weight  w,  or  resis- 
tance, will  occupy  its  proportional  part  of  the  velocity. 
That  is,  if  w  be  =z  i  P,  the  velocity  with  which  P  will 
then  descend,  will  be  §  16=8  feet  per  second. 

5.  If  w  be  =  P,  there  can  be  no  velocity,  consequent- 
ly no  effect ;  and  if  w  =  o  then  P  will  descend  16  ^eet 
in  a  second,  but  produces  no  effect ;  because,  the  power, 
although  1600  per  second,  is  applied  to  hoist  nothing. 

Upon  these  principles  1  have  calculated  the  following 
scale. 


Chap.  11.] 


MECHANICS. 


57 


A  SCALE 


DETERMINING  THE  MAXIMUM  CHARGE, 


i'i.  I. 


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^  MECHANICS.  [Chap.  11. 

By  this  scale  it  appears,  that  when  the  weight  w  is 
=50=  I  P  the  power ;  the  eiFect  is  at  a  maxiinum,  viz. 
400,  as  appears  in  the  6th  column,  when  the  velocity  is 
half  the  natural  velocity,  viz.  8  feet  per  second  ;  and 
then  the  ratio  of  the  power  to  the  effect  is  as  10  to  5,  as 
appears  in  the  8th  line. 

By  this  scale  it  appears,  that  all  engines  that  are 
moved  by  one  constant  power,  which  is  equably  acce- 
lerated in  their  velocity  (if  any  such,  there  be)  as  appears 
to  be  the  case  here,  must  be  charged  with  weight  or  re- 
sistance equal  to  half  the  moving  power,  in  order  to 
produce  the  greatest  effect  in  a  given  time  ;  but  if  time 
be  not  regarded,  then  the  greater  the  charge,  so  as  to 
leave  any  velocity,  the  greater  the  effect,  as  appears  by 
the  8th  column.  So  that  it  appears,  that  an  overshot 
wheel,  if  it  be  made  immensely  capacious,  and  to  move 
very  slow,  may  produce  effects  in  the  ratio  of  9,9  to  10 
of  the  power. 


ART.    37. 


SCALE  OF  EXPERIMENTS. 


The  following  scale  of  actual  experiments  were  made 
to  prove  whether  the  resistance  occupies  its  proportion 
of  the  velocity,  in  order  that  I  might  judge  whether  the 
foregoing  scale  was  founded  on  true  principles ;  the  ex- 
periments were  not  very  accurately  performed,  but  often 
repeated,  and  proved  always  nearly  the  same.  See  Plate 
11.  fig.  18. 


Chap.  11.] 


MECHANICS. 


59 


A  SCALE 


EXPERIMENTS. 


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" 

.     3^ 

o' 

C 
p 

•   3" 

o 

3 

o  « 
2.« 
^2. 

r* 

•    c  3 

.     3 

.    f» 

^orij 

cr 
n 

^P 

O 

re 

o 

d; 

7 

40 

7 

0 

0 

6 

20 

2X6 

12 

14 

10  :  8.5 

24 

5 

15.5 

2.6X5 

13 

18.2 

10  :  7.1 

33.8 

4 

12 

3.33x4 

13.32 

23.31 

10  :  5.7 

44.35 

3.5 

10 

4X3.5 

14 

28 

10  :  5. 

maximum 
new  theory. 

3 

9 

4  44x3 

13.32 

31.08 

10  :  42 

59.14 

2 

6.5 

5X2 

12 

42 

10  :  28 

72  maximum. 

1 

6 

5.6X1 

6.6 

46.2 

10  :  1.4 

33.56 

■— 

0 

5 

3 

0 

56 

60  MECHANICS.  [Chap.  II. 

By  this  scale  it  appears,  that  when  the  power  P  falls 
freely  without  any  load,  it  descends  40  feet  in  five  equal 
parts  of  time,  but,  when  charged  with  3,51bs.=iP,  which 
was  7lbs.  it  then  took  up  10  of  those  parts  of  time  to  de- 
scend the  same  distance ;  which  seems  to  shew,  that  the 
charge  occupies  its  proportional  part  of  the  whole  velo- 
city, which  was  wanted  to  be  known,  and  the  maximum 
appears  as  in  the  last  scale.*  It  also  shews,  thai  the  ef- 
fect is  not  as  the  weight  multiplied  into  the  square  of  its 
ascending  velocity,  this  being  the  measure  of  the  effect 
that  would  be  produced  by  the  stroke  on  a  non-elastic 
body. 

This  experiment  partly  confirmed  me  in  what  I  have 
called  the  New  Theory ;  but  still  doubting,  and  after  I 
had  formed  the  foregoing  tables,  I  called  on  the  late  in- 
genious and  worthy  friend,  William  Waring,  teacher  in 
the  Friends'  Academy,  Philadelphia,  for  his  assistance. 
He  told  me  he  had  discovered  the  error  in  the  old  theory 
and  corrected  it  in  a  paper  which  he  had  laid  before  the 
Philosophical  Society  of  Philadelphia,  wherein  he  had 
shewn  that  the  velocity  of  the  undershot  water-wheel,  to 
produce  a  maximum  effect,  must  be  just  one  half  the  ve- 
locity of  the  M'ater. 


ART.    38. 
WILLIAM  WARING'S  THEORY. 

The  following  are  extracts  from  the  above  mentioned 
paper,  published  in  the  third  volume  of  the  Transactions 
of  the  American  Philosophical  Society,  held  at  Philadel- 
phia, p.  144. 

After  his  learned  and  modest  introduction,  in  which 
he  shews  the  necessity  of  correcting  so  great  an  error  as 
the  old  theory,  he  begins  with  these  words,  viz. 

"  But  to  come  to  the  point,  I  would  just  premise  these 

*  Since  writinp  the  above,  I  have  seen  Atwood's  Treatise  on  Motion, 
wherein  he  gives  a  set  of  accurate  experiments,  to  prove  (beyond  doubt) 
that  ihe  conclusion  I  have  drawn  is  riglit,  viz.  That  the  charge  occupies  its 
proportional  part  of  the  whole  velocity.  See  the  American  Encyclopedias 
vol.  X.  p.  786. 


Chap.  11.]  MECHANICS.  61 

DEFINITIONS. 

If  a  stream  of  water  impinge  against  a  wheel  in  motion, 
there  are  three  different  velocities  to  be  considered  ap- 
pertaining thereto,  viz. 

First,  The  absolute  velocity  of  the  water. 

Second,  The  absolute  velocity  of  the  wheel. 

Third,  the  relative  velocity  of  the  water  to  that  of 
the  wheel;  i.  e.  the  difference  of  the  absolute  velocities, 
or  the  velocity  with  which  the  water  overtakes  or  strikes 
the  wheel. 

Now  the  mistake  consists  in  supposing  the  momentum, 
or  force  of  the  water  against  the  wheel,  to  be  in  the  du- 
plicate ratio  of  the  relative  velocit}^;  Whereas, 

PROP.  I. 

The  force  of  an  invariable  stream,  impinging  against  a 
mill-wheel  in  motion,  is  in  the  simple  proportion  of  the 
relative  velocity. 

For,  if  the  relative  velocity  of  a  fluid  against  a  single 
plane,  be  varied,  either  by  the  motion  of  the  plane  or  of 
the  fluid  from  a  gi^'en  aperture,  or  both,  then  the  number 
cr  particles  acting  on  the  plane,  in  a  given  time,  and  like- 
wise the  momentum  of  each  particle  being  respectively 
as  the  relative  velocity,  the  force,  on  both  these  accounts, 
must  be  in  the  duplicate  ratio  of  the  relative  velocity, 
agreeable  to  the  common  theory,  with  respect  to  this  sin- 
gle plane ;  but  the  number  of  these  planes  or  parts  of  the 
wheel,  acted  on  in  a  given  time,  will  be  as  the  velocity 
of  the  wheel,  or  inversely  as  the  relative  velocity ;  there- 
fore the  moving  force  of  the  wheel  must  be  as  the  simple 
ratio  of  the  relative  velocity.  Q.  E.  D. 

Or  the  proposition  is  manifest  from  this  consideration, 
that  while  the  stream  is  invariable,  whatever  be  the  ve- 
locity of  the  wheel,  the  same  number  of  particles,  or 
quantity  of  the  fluid,  must  strike  it  somewhere  or  other 
in  a  given  time ;  consequently,  the  variation  of  the  force 
is  only  on  account  of  the  varied  impingent  velocity  of 
the  same  body,  occasioned  by  a  change  of  motion  in 
the  wheel;  that  is,  the  momentum  is  as  the  relative 
velocitv. 


62  MECHANICS.  [Chap.  11. 

Now  this  true  principle,  substituted  for  the  erroneous 
one  in  use,  will  bring  the  theory  to  agree  remarkably 
with  the  notable  experiments  of  the  ingenious  Smeaton, 
published  in  the  Philosophical  Transactions  of  the  Royal 
Society  of  London,  for  the  year  1751,  vol.  51;  for  which 
the  honorary  annual  medal  was  adjudged  by  the  so- 
ciety, and  presented  to  the  author  by  their  president. 

An  instance  or  two  of  the  importance  of  this  correction 
may  be  adduced,  as  follows : 


PROP.  II. 

The  velocity  of  a  wheel,  moved  by  the  impact  of  a 
stream,  must  be  half  the  velocity  of  the  fluid,  to  produce 
the  greatest  effect  possible. 

C  V=the  velocity,  M=the  momentum,  of  the  fluid. 

^  v=:the  velocity,  P=the  power,  of  the  wheel. 

Then  V — v=their  relative  velocity,  by  definition  3d. 
M    

And,  as  V:V— v::M:— xV--v=P,  (Prop.  1.)  which 

M 

xt=P,  v= — xVv — v^=a  maximum;  hence  Vv — v'= 

V 
a  maximum  and  its  fluxion  (v  being  a  variable  quantity) 
=Vv — 2vv=o;  therefore=|V;  that  is,  the  velocity  of 
the  wheel=:half  that  of  the  fluid,  at  the  place  of  impact, 
when  the  effect  is  a  maximum.  Q.  E.  D. 

The  usual  theory  gives  v=4V,  where  the  error  is  not 
less  than  one  sixth  of  the  true  velocity. 


Wm.  waring. 


Philadelphia^  7th 
9th  mo.  1790. 


Note,  I  omit  quoting  prop.  III.  as  it  is  in  algebra,  and 
refers  to  a  figure,  because  I  am  not  vnriting  so  particular- 
ly to  men  of  science,  as  to  practical  mechanics. 


Chap.  11.]  MECHANICS.  63 

ART.    39. 

Extract  from  a  further  paper ^  read  in  the  Philosophical 
Society,  April  5th,  1793. 

"  Since  the  Philosophical  Society  were  pleased  to 
favour  my  crude  observations  on  the  theory  of  mills, 
with  a  publication  in  their  transactions,  I  am  apprehen- 
sive some  part  thereof  may  be  misapplied,  it  being  there- 
in demonstrated,  that '  the  force  of  an  invariable  stream, 
impinging  against  a  mill-wheel  in  motion,  is  in  the  sim- 
ple direct  ratio  of  the  relative  velocity.'  Some  may  sup- 
pose that  the  effect  produced,  should  be  in  the  same 
proportion,  and  either  fall  into  an  error,  or  finding  by 
experiment,  the  effect  to  be  as  the  square  of  the  velocity, 
conclude  the  new  theory  to  be  not  well  founded  ;  I  there- 
fore wish  there  had  been  a  little  added,  to  prevent  such 
misapplication,  before  the  Society  had  been  troubled  with 
the  reading  of  my  paper  on  that  subject :  perhaps  some- 
thing like  the  following. 

The  maximum  effect  of  an  undershot  wheel,  produ- 
ced by  a  given  quantity  of  water,  in  a  given  time,  is  in 
the  duplicate  ratio,  of  the  velocity  of  the  water  :  for  the 
effect  must  be  as  the  impetus  acting  on  the  wheel,  mul- 
tiplied into  the  velocity  thereof:  but  this  impetus  is 
demonstrated  to  be  simply  as  the  relative  velocity.  Prop. 
I.  and  the  velocity  of  the  wheel,  producing  a  maximum, 
being  half  of  the  water  by  Prop.  II.  is  likewise  as  the 
velocity  of  the  water;  hence  the  power  acting  on  the 
wheel,  multiplied  into  the  velocity  of  the  wheel,  or  the 
effect  produced,  must  be  in  the  duplicate  ratio  of  the 
velocity  of  the  water.     Q.  E.  D. 

CoROL.  Hence  the  effect  of  a  given  quantity  of  wa- 
ter, in  a  given  time,  will  be  as  the  height  of  the  head, 
because  this  height  is  as  the  square  of  the  velocity.  This 
also  agrees  with  experiment. 

If  the  force,  acting  on  the  wheel,  were  in  duplicate 
ratio  of  the  water's  velocity,  as  usually  asserted,  then  the 
effect  would  be  as  the  cube  thereof,  when  the  quantity 
of  water  and  time  are  given,  \^•hich  is  contrary  to  the 
result  of  experiment.'' 


64.  MECHANICS.  [Chap.  11 

ART.    40. 
WAKING'S  THEORY  DOUBTED. 

From  the  time  I  first  called  on  William  Waring,  un- 
til I  read  his  publication  on  the  subject,  (after  his  death) 
I  had  rested  partly  satisfied,  with  the  new  theory,  as  I 
have  called  it,  with  respect  to  the  velocity  of  the  wheel, 
at  least;  but  finding  that  he  had  not  determined  the 
charge,  as  well  as  the  velocity,  by  which  we  might 
have  compared  the  ratio  of  the  power  and  the  effect  pro- 
duced, and  that  he  had  assigned  reasons  somewhat  dif- 
ferent for  the  error  ;  and  having  found  the  motion  to  be 
rather  too  slow  to  agree  with  practice,  I  began  to  suspect 
the  whole,  and  resumed  the  search  for  a  true  theory, 
thinking  that  perhaps  no  person  had  ever  yet  considered 
every  thing  that  affects  the  calculation,  I  therefore  pre- 
mised the  following 

POSTULATES. 

1.  A  given  quantity  of  perfect,  elastic  or  solid  matter, 
impinging  on  a  fixed  obstacle,  its  effective  force  is  as  the 
squares  of  its  different  velocities,  although  its  instant 
force  may  be  as  its  velocities  simply,  by  annotation, 
art.  8.*    ' 

2.  An  equal  quantity  of  elastic  matter,  impinging  on 
a  fixed  obstacle  with  a  double  velocity,  produces  a  quad- 
ruple effect,  art.  8 ;  i.  e.  their  effects  are  as  the  squares 
of  their  velocities.     Consequendy, 

3.  A  double  quantity  of  said  matter,  impinging  with 
a  double  velocity,  produces  an  octuble  effect,  or  their 
effects  are  as  the  cubes  of  their  velocities,  art.  47  and  67. 

4.  If  the  impinging  matter  be  non-elastic,  such  as 
fluids,  then  the  instant  force  will  be  but  half  in  each 
case,  but  the  ratio  will  be  the  same  in  each  case. 

5.  A  double  velocity,  through  a  given  aperture,  gives 
a  double  quantity  to  strike  the  obstacle  or  wheel,  there- 
fore the  effects,  by  postulate  3,  will  be  as  the  cubes  of 
the  velocity.     See  art.  47. 

*  Because  the  distance  it  will  recede  after  the  stroke  through  any  re- 
sisting medium,  will  be  as  the  squares  of  its  impinging  velocities. 


Ghap.  11.]  MECHANICS.  65 

6.  But  a  double  relative  velocity  cannot  increase  the 
quantity  that  is  to  act  on  the  wheel,  therefore  the  effect 
can  only  be  as  the  square  of  the  velocity,  by  postulate  2. 

7.  Although  the  instant  force  and  effects  of  striking 
fluids  on  fixt  obstacles,  are  only  as  their  simple  velocities, 
yet  their  effects,  on  moving  wheels,  are  as  the  squares  of 
their  velocities;  because,' 1,  a  double  striking  velocity 
gives  a  double  instant  force,  which  bears  a  double  load 
on  the  wheel ;  and  2,  a  double  velocity  moves  the  load 
a  double  distance  in  an  equal  time,  and  a  double  load 
moved  a  double  distance,  is  a  quadruple  effect. 


ART.    41. 
SEARCH  FOR  A  TRUE  THEORY,  COMMENCED  ON  A  NEW  PLAN. 

It  appears  that  we  have  applied  wrong  principles  in 
our  search  after  a  true  theory  of  the  maximum  velocity 
and  load  of  undershot  water-wheels,  or  other  engines 
moved  by  a  constant  power,  that  does  not  increase  or 
decrease  in  quantity  on  the  engine,  as  on  an  overshot 
water-wheel,  as  the  velocity  varies. 

Let  us  suppose  water  to  issue  from  under  a  head  of  16 
feet,  on  an  undershot  water-wheel:  then,  if  the  wheel 
moves  freely  with  the  water,  its  velocity  will  be  32,4  feet 
per  second,  but  will  bear  no  load. 

Again,  suppose  we  load  it,  so  as  to  reduce  its  motion 
to  be  equal  the  velocity  of  water  spouting  from  under 
15  feet ;  it  appears  evident  that  the  load  will  then  be  just 
equal  to  that  1  foot  of  the  head,  the  velocity  of  which  is 
checked ;  and  this  load  multiplied  into  the  velocity  of 
the  wheel,  viz.  31,34x1=31,34  for  the  effect. 

This  appears  to  be  the  true  principle,  from  which  we 
must  seek  the  maximum  velocity  and  load,  for  such  en- 
gines as  are  moved  by  one  constant  power;  and  on  this 
principle  I  have  calculated  the  following  scale. 


66  MECHANICS.  [Chap.  11. 

A  SCALE 

FOR    SETEBIUIIVINO    THE  ' 

TRUE  MAXIMUM  VELOCITY  AND  LOAD 

FOR 

UNDERSHOT  WHEELS. 


S 

< 

r 

w 

^ 

ft 
o 

elocity 
cond, 
the  W! 
unbal 

oad  o 
parti 
whic 

flfect 
of   t 
load. 

s 

_  -*» 

3-  3     -»J 

3-3 

is 

S;     » 

-*3 

(t    ft 

oft 
beii 
ter 
ncei 

r>  n  '^ 

^    S 

0. 
o 

§  5 

^3^S- 

%l% 

cr  ft 
re   n 
ft    o 

wheel 
equal 
n  und 

3V 

•z 

f8    3 

-    s 

-1^ 

^ 

—  O 

ft     <!    " 

rt  ft 

S'  5" 

o 

n 

;?  ft 

'•L'O 

&<  ft 

^, 

c 

tr  ■r-" 

3  c 

3' 

o 

per  se 
acity  0 
ead  lef 

o  ^ 

•^l 

crtj 

•< 

5'  ^ 

O    w 

o 
"  2. 

fD 

-  -^  • 

-r,  r^ 

ft  ■< 

f.e. 

tef*  1 

feet. 

16 

16 

32-4 

0 

0 

15 

31.34 

1 

3134 

14 

30  2 

2. 

60  4 

12 

28 

4. 

112 

10 

25.54 

6 

153.24 

8 

22  8 

8 

182.4 

7 

2143 

9 

192.87 

6 

19.84 

10 

198.4 

5.66 

19.27 

1033 

198.95 

5.33 

18.71 

10.66 

199  44 

Maximum  motion 

5 

18. 

11 

198 

and  load. 

4 

16.2 

12 

194  4 

3 

14. 

IS 

172 

2 

11,4 

14 

159.6 

1 

81 

15 

120. 

0 

0 

16 

0 

Chap.  11.]  MECHANICS.  67 

In  this  scale  let  us  suppose  the  aperture  of  the  gate  to 
be  a  square  foot;  then  the  greatest  load  that  will  balance 
the  head,  will  be  16  cubic  feet  of  water,  and  the  different 
loads  will  be  shewn  in  cubic  feet  of  water. 

And  then  it  appears,  by  this  scale,  that  when  the 
wheel  is  loaded  with  10,66  cubic  feet  of  water,  just  2-3 
of  the  greatest  load,  its  velocity  will  be  18,71  feet  per 
second,'  just  ,577  parts  of  the  velocity  of  the  water,  and 
the  effect  produced  is  at  a  maximum,  or  the  greatest  pos- 
sible, viz.   199,44. 

To  make  this  more  plain,  let  us  suppose  A  B,  plate 
II,  fig.  19,  to  be  a  fall  of  water  16  feet,  which  we  wish 
to  apply  to  produce  the  greatest  effect  possible,  by  hoist- 
ing water  on  its  side  opposite  to  the  power  applied ;  first, 
on  the  undershot  principle,  where  the  water  acts  by  its 
impulse  only.  Now  let  us  suppose  the  water  to  strike 
the  wheel  at  I,  then,  if  we  let  the  wheel  move  freely 
without  any  load,  it  will  move  with  the  velocity  of  the 
water,  viz.  32,4  feet  per  second,  but  will  produce  no 
effect,  if  the  water  issue  at  C ;  although  there  be  32,4 
cubic  feet  of  water  expended,  under  16  feet  perpendicu- 
lar descent.  Let  the  weight  of  a  cubic  foot  of  water  be 
represented  by  unity  or  1,  for  ease  in  counting;  then 
32,4>:  16  will  show  the  power  expended,  per  second,  viz. 
518,4;  and  the  water  it  hoists  multiplied  into  its  per- 
pendicular ascent,  or  height  hoisted,  will  shew  the  effect. 
Then,  in  order  to  obtain  effect  from  the  power,  we  load 
the  wheel;  the  simplest  way  of  doing  which,  is,  to  cause 
the  tube  of  water  C  D  to  act  on  the  back  of  the  bucket 
at  I;  then,  if  CD  be  equal  to  AB,  the  wheel  will  be  held 
in  equihbrio;  this  is  the  greatest  load,  and  the  whole  of 
the  fall  AB  is  balanced,  and  no  part  left  to  give  the 
wheel  velocity;  therefore  the  effect=0.  But  if  we  make 
CD=12  feet  of  AB,  then  from  4  to  A=4  feet,  is  left  un- 
balanced, to  give  velocity  to  the  wheel,  which  is  now 
loaded  with  12  feet,  and  exactly  balanced  by  12  on  the 
other  side,  and  perfectly  free  to  move  either  way  by  the 
least  force  applied:  Therefore  it  is  evident,  that  the 
whole  pressure  or  force  of  4  feet  of  AB  will  act  to  give 
velocity  to  the  wheel,  and,  as  there  is  no  resistance  to 
oppose  the  pressure  of  these  4  feet,  the  velocity  will  be 


68  MECHANICS.  [Chap.  11. 

the  same  that  water  will  spout  from  under  4  feet  head, 
viz.  16,2  feet  per  second,  which  is  shewn  by  the  hori- 
zcntal  line  4=16,2,  and  the  perpendicular  line  12=12 
rejnesents  the  load  of  the  wheel;  the  rectangle  or  pro- 
duct of  these  tu  o  lines,  form  a  parallelogram,  the  area  of 
\\hich  is  a  true  representation  of  the  effect,  viz.  the  load 
12  multiplied  into  16,2  the  distance  it  moves  per  second 
=  194,4,  the  effect.  In  like  manner  w^e  may  try  the  ef- 
fect of  different  loads ;  the  less  the  load,  the  greater  will 
be  the  velocity.  The  horizontal  lines  all  shew  the  velo- 
city of  the  wheel,  produced  by  the  respective  heads  left 
unbalanced,  and  the  perpendicular  lines  shew  the  load  on 
the  M  heel ;  and  we  find,  that  when  the  load  is  10,66=|16, 
the  load  at  equilibrio,  the  velocity  of  the  wheel  \\\\l  be 
18,71  feet  per  second,  which  is  -^^-^^^-^  parts,  or  a  little  less 
than  6  tenths,  or  |  the  velocity  ot  the  water,  and  the  effect 
is  199,44  the  maximum  or  greatest  possible;  and  if  the 
aperture  of  the  gate  be  1  foot,  the  quantity  will  be  18,71 
cubic  feet  per  second.  The  power  being  18,71  cubic 
feet  expended  per  second,  multiplied  by  16  feet  the  per- 
pendicular descent,  produces  299,36,  and  the  ratio  of  the 
power  and  effect  being  10  to  6-j\,  or  as  3  :  2;  but  this  is 
sup]:)osing  none  of  the  force  lost  by  non-elasticity. 

This  may  appear  plainer,  if  we  suppose  the  water  to 
descend  the  tube  A  B,  and,  by  its  pressure,  to  raise  the 
water  in  the  tube  C  D;  now  it  is  evident,  that  if  we  raise 
the  water  to  D,  we  have  no  velocity,  therefore  effect=0. 
Then  again,  if  we  open  the  gate  at  C,  we  have  32,4  feet 
per  second  velocity,  but  because  we  do  not  hoist  the  wa- 
ter any  distance,  effect=0.  Therefore,  the  maximum  is 
somewhere  between  C  and  D.  Then  suppose  we  open 
gates  of  1  foot  area,  at  different  heights,  the  velocity  v/nl 
shew  the  quantity  of  cubic  fefit  raised ;  \^  hich  multiplied 
by  the  perpendicular  height  of  the  gate  from  C,  or 
height  raised,  gives  the  effect  as  before,  and  the  maxi- 
mum as  before.  But  here  we  must  consider,  that  in 
both  these  cases  the  water  acts  as  a  perfect  definite 
quantity,  which  will  produce  effects  equal  to  elastic  bo- 
dies, or  equal  to  its  gravity  (see  art.  59),  which  is  im- 
practicable in  practice:  Whereas,  when  it  acts  by  per- 
cussion only,  it  communicates  only  half  of  its  original 


Chap.  11.]  MECHANICS.  69 

force,  on  account  of  its  non-elasticity,  the  other  half  be- 
ing spent  in  splashing!;  about  (see  art.  8);  therefore  the 
true  effect  will  be  j-^-^  (a  little  more  than  1-3)  of  the  mov- 
ing power;  because  near  1-3  is  lost  to  obtain  velocity, 
and  half  of  the  remaining  2-3  is  lost  by  non- elasticity. 
These  are  the  reasons,  why  the  eifects  produced  by  an 
undershot  wheel  is  only  half  of  that  produced  by  an 
overshot  wheel,  the  perpendicular  descent  and  quantity 
of  water  being  equal.  And  this  agrees  with  Smeaton's 
experiments  (see  art.  68);  but  if  we  suppose  the  velocity 
of  the  wheel  to  be  one-third  that  of  the  water=10,8,  and 
the  load  to  be  4-9  of  16,  the  greatest  load  at  equilibrio; 
which  is=7,lll,  as  by  old  theory,  then  the  effect  will  be 
10,8x4,9  of  16=76,79  for  the  effect,  which  is  quite  too 
little,  the  moving  power  being  32,4  cubic  feet  of  Avater, 
multiplied  by  16  feet  descent=518,4,  the  effect  by  this 
theory  being  less  than  -^-^-^  of  the  poA^er,  about  half  equal 
to  the  effect  by  experiment,  which  effect  is  set  on  the 
outside  of  the  dotted  circle  in  the  fig.  (19).  The  dotted 
lines  join  the  corner  of  the  parallelograms,  formed  by  the 
lines  that  represent  the  loads  and  velocities,  in  each  ex- 
periment or  supposition,  the  areas  of  which  truly  repre- 
sent the  effect,  and  the  dotted  line  A  a  d  x,  meeting  the 
perpendicular  line  x  E  in  the  point  x,  forming  the  paral- 
lelogram ABCx,  truly  represents  the  power=518,4. 

Again,  if  we  suppose  the  w  heel  to  move  with  half  the 
velocity  of  the  water,  viz.  16,2  feet  per  second,  and  be 
loaded  with  half  the  greatest  load=8,  according  to  War- 
ing's  theory,  then  the  effect  will  be  16,2x8=129,6  for 
tlie  effect,  about  -^^\  of  the  power,  which  is  still  less  than 
by  experiment.  All  this  seems  to  confirm  the  maximum 
brought  out  on  the  new  principles. 

But,  if  we  suppose,  according  to  the  new  principle, 
that,  when  the  wheel  moves  with  the  velocity  of  16,2 
feet  per  second,  which  is  the  velocity  of  a  4  feet  head, 
that  it  will  then  bear  as  a  load  the  remaining  12  feet, 
then  the  effect  will  be  16,2x12=194,4,  which  nearly 
agrees  with  practice:  but  as  most  mills  in  practice 
move  faster,  rather  than  slower,  than  what  I  call  the 
true  maximum,  shews  it  to  be  nearest  the  truth,  the 
true  maximum  velocity  being  ,577  of  the  velocity  of  the 


to  MECHANICS.  [Chap.  11. 

water,  and  the  mills  in  practice  moving  with  2-.3,  and 
generally  quicker.* 

This  scale  also  establishes  a  true  maximum  charge 
for  an  overshot  wheel,  when  the  case  is  such,  that  the 
power  or  quantity  of  water  on  the  wheel  at  once,  is  al- 
ways the  same,  even  although  the  velocity  vary,  which 
would  be  the  case,  if  the  buckets  were  kept  always  full : 
for,  suppose  the  water  to  be  shot  into  the  wheel  at  a,  and 
by  its  gravity  to  raise  the  whole  water  again  on  the  oppo- 
site side ;  then,  as  soon  as  the  water  rises  in  the  wheel 
to  d,  it  is  evident  that  the  wheel  vvill  stop,  and  effect=0 ; 
therefore  we  must  let  the  water  out  of  the  wheel,  before 
it  rises  to  d,  which  will  be  in  effect  to  lose  part  of  the 
power  to  obtain  velocity.  If  the  buckets  both  descen- 
ding and  ascending,  carry  a  column  of  water  1  foot  square, 
then  the  velocity  of  the  wheel  will  shew  the  quantity 
hoisted  as  before,  which,  multiplied  by  the  perpendicular 
ascent,  shews  the  effect,  and  the  quantity  expended,  mul- 
tiplied bv  the  perpendicular  descent  shows  the  power; 
and  we  find,  that  when  the  wheel  is  loaded  with  2-3  of 
the  power,  the  effect  will  be  at  a  maximum,  i.  e.  the  whole 
of  the  water  is  hoisted,  2-3  of  its  whole  descent,  or  2-3  of 
the  water  the  whole  of  the  descent,  therefore  the  ratio  of 
the  pcjwerto  the  effect  is  as  3  to  2,  double  to  the  effect  of 
an  undershot  wheel ;  but  this  is,  supposing  the  quantity  in 

•  The  reason  why  the  wheel  bears  so  great  a  load  at  a  maximum,  ap- 
pears 10  be  as  follows,  viz. 

A  16  feet  head  of  water  over  a  gate  of  1  foot,  issues  32,4  cubic  feet  of 
wuier  in  a  second,  to  strike  the  wheel  in  the  same  time,  that  a  heavy  body 
W'il  lake  up  in  filling  through  the  height  of  the  head.  Now  if  16  cubic 
feet  ofeliistic  nnaiter,  was  to  fall  16  feet,  and  s  rike  an  elastic  plane,  it  wonld 
rise  by  the  force  of  the  stroke,  to  the  height  from  whence  it  fell;  or,  in 
other  words,  it  will  have  force  sufficient,  to  bear  a  load  of  16  cubic  feet. 

Again,  if  32  cubic  feet  of  non  elastic  matter,  moving  with  the  same  veio- 
city,  (with  vi>  hich  the  16  feet  of  elastic  matter  struck  the  plane)  strike  a 
w':eel  in  the  same  time,  alihough  it  communicate  only  half  the  force,  that 
gave  \\  motion;  yet,  because  there  is  a  double  quantity  striking  in  the 
same  time,  the  effects  will  be  equal,  that  is,  it  will  bear  a  load  of  16  cubic 
feel,  or  the  whole  column  to  hold  it  in  equilibrio. 

Again,  to  check  the  whole  velocity,  req  lires  the  whole  column,  that  pro- 
duces  the  velocity,  consequently,  to  check  any  part  of  the  velocity,  will  re- 
quire  such  a  part  of  the  column  that  produces  the  part  checked;  and  we 
find  by  art.  41,  that,  to  check  the  velocity  of  the  wheel,  to  be  ,577  of  the 
velocity  of  the  water,  it  requires  2  3  of  the  whole  column,  and  this  is^the 
maximum  load  When  the  velocity  of  the  wheel,  is  multiplied  by  2^3  of 
the  col  mn,  it  produces  the  effect,  which  will  be  to  the  power,  as  38  to 
100  ;  or  as  3,8  to  10.  somewhat  more  than  1-3,  and  the  friction  and  resist- 
ance of  the  air  may  reduce  it  to  1-3. 


Chap.  11.}  MECHANICS.  Ti 

tlie  buckets  to  be  always  the  same  ;  whereas,  in  overshot 
wheels,  the  quantity  in  the  buckets  is  inversely  as  the  velo- 
city of  the  u  heel,  i.  e.  the  slower  the  motion  of  the  wheel, 
the  greater  the  quantity  in  the  buckets,  and  the  greater  the 
velocity  the  less  the  quantity  ;  but,  again,  as  we  are  oblig- 
ed to  let  the  overshot  wheel  move  with  a  considerable  ve- 
locity, in  order  to  obtain  a  steady,  regular  motion  to  the 
mill,  we  will  find  this  charge  to  be  always  nearly  right  x 
hence  I  deduce  the  following  theory. 


ART.    4S. 

THEORY. 

A  TRUE  THEORY  DEDUCED. 

This  scale  seems  to  have  shewn, 

1.  That  when  an  undershot  mill  moves  with  ,577  cd 
nearly  ,6  of  the  velocity  of  the  water,  it  will  then  bear 
a  charge,  equal  to  2-3  of  the  load,  that  will  hold  the 
wheel  in  equilibrio,  and  then  the  effect  will  be  at  a  maxi- 
mum. The  ratio  of  the  power  to  the  effect  will  be  as  S 
to  1,  nearly. 

2.  That  when  an  overshot  wheel  is  charged  with  2-S 
of  the  weight  of  the  water  acting  upon  the  wheel,  then 
the  effect  will  be  at  a  maximum,  i.  e.  the  greatest  effect, 
that  can  be  produced  by  said  power  in  a  given  time,  and 
the  ratio  of  the  power  to  the  effect  will  be  as  3  to  2, 
nearly. 

3.  That  1-3  of  the  power  is  necessarily  lost  to  obtain 
velocity,  or  to  overcome  the  vis  inertia  of  the  matter,  and 
this  will  hold  true  with  all  machinery  that  requires  velo- 
city as  well  as  power.  This  I  believe  to  be  the  true 
theory  of  water-mills,  for  the  following  reasons,  viz. 

1.  The  theory  is  deduced  from  original  reasoning, 
without  depending  much  on  calculation. 

2.  It  agrees  better  than  any  other  theory,  with  the  in- 
genious Smeaton's  experiments. 

3.  It  agrees  best  with  real  practice,  from  the  best  of 
my  information. 


72  MECHANICS.  [Chap.  IK 

Yet  I  do  not  wish  any  person  to  receive  it  implicitly, 
without  first  informing  himself,  whether  it  be  well  found- 
ed, and  agrees  with  practice  :  for  this  reason  I  have 
quoted  said  Smeaton's  experiments  at  full  length,  in 
this  work,  that  the  reader  may  compare  them  with  the 
theory. 

true  theorem  for  finding  the  maximum  charge  for 
undp:rshot  wheels 

As  the  square  of  the  velocity  of  the  water  or  wheel 
empty,  is  to  the  height  of  the  head,  or  pressure,  v»hich 
produced  that  velocity,  so  is  the  square  of  the  velocity 
of  the  wheel,  loaded  to  the  head,  pressure,  or  force, 
which  will  produce  that  velocity  ;  and  this  pressure,  de- 
ducted from  the  whole  pressure  or  force,  will  leave  the 
load  moved  by  the  wheel,  on  its  periphery  or  verge, 
which  load,  multiplied  by  the  velocity  of  the  wheel, 
shews  the  effect. 

PROBLEM. 

Let  V=32,4,  the  velocity  of  the  water  or  wheel, 

P=16,  the  pressure,  force,  or  load,  at  equilibrio, 
v=the  velocity-  of  the  wheel,  supposed  to  be  16,2 

feet  per  second, 
p=the  pressure,  force  or  head,  to  produce  said  ve- 
locity, 
l=the  load  on  the  wheel. 
Then  to  find  1,  the  load,  we  must  first  find  p ; 
Then,  by 

Theorem  VV :  P::vv:p, 
And  P— p=l 
VVp=vvP 
vvP 
p=VV=4 
l=P—p=12,  the  load. 
Which,  in  words  at  lens^th,  is,  the  square  of  the  veloci- 
ty of  the  M  heel,  multiplied  by  the  whole  force,  pressure, 
or  head  of  the  water,  and  divided  by  the  square  of  the 
velocity  of  the  water,  quotes  the  pressure,  force,  or  head 
of  water,  that  is  left  unbalanced  by  the  load,  to  produce 
the  velocity  of  the  wheel,  which  pressure,  force  or  head, 


Chap.  ll.J  MECHANICS.  TS 

subtracted  from  the  whole  pressure,  force  or  head,  leaver 
the  load  that  is  on  the  wheel. 


ART.    43. 

Theorem  for  finding  the  velocity  of  the  wheels  when  xve 
have  the  velocity  of  the  water,  Load  at  equilibrio,  and 
Load  on  the  wheel  given. 

As  the  square  root  of  the  whole  pressure,  force  or  load 
at  equilibrio,  is  to  the  velocity  of  the  water,  so  is  the 
square  root  of  the  difference,  between  the  load  on  the 
wheel,  and  the  load  at  equilibrio,  to  the  velocity  of  the 
wheel. 

PROBLEM. 

Let  V=: velocity  of  the  water=32,4, 

P= pressure,  force,  head,  or  load  at  equilibrio=.16', 
l=the  load  on  the  wheel,  suppose  12, 
v=velocity  of  the  wheel. 

Then  by  the  

Theorem  yP: V:: y/P— l:v 
And  v'Pxv=Vv/P— 1 
VyP— 1 

v= =-«-=16,2.    C  The  velocity  of  th€ 

v'P  \  wheel. 

That  is,  in  words  at  length,  the  velocity  of  the  water 
32,4,  multiplied  by  the  square  root  of  the  difference,  be- 
tween the  load  on  the  wheel,  12,  and  the  load  at  equili- 
brio 16=2=64,8,  divided  by  the  square  root  of  the  load 
at  equilibrio,  quotes  16,2,  the  velocity  of  the  wheel. 

Now,  if  we  seek  for  the  maximum,  by  either  of  these 
theorems,  it  will  be  found  as  in  the  scale,  fig.  19. 

Perhaps  here  may  now  appear  the  true  cause  of  the 
error  of  the  old  theory,  art.  35,  by  supposing  the  load  on 
the  wheel,  to  be  as  the  square  of  the  relative  velocity,  of 
the  water  and  wheel. 

K 


74  MECHANICS.  [Chap.  11. 

And  of  the  error  of  what  I  have  called  the  new  the- 
ory, by  supposing  the  load  to  be  in  the  simple  ratio  of 
the  relative  or  striking  velocity  of  the  water,  art.  38 ; 
whereas  it  is  to  be  found  by  neither  of  these  propor- 
tions. 

Neither  the  old  nor  new  theories  agree  with  practice  ; 
therefore  we  may  suspect  they  are  founded  on  error. 

But  if  what  I  call  the  true  theory,  should  continue  to 
agree  with  practice,  the  practitioner  need  not  care  on 
what  it  is  founded. 


ART.    44. 

Of  the  Maximum  velocity  for  Overshot  Wheels^  or  those 
that  are  moved  by  the  weight  of  the  Water. 

Before  I  dismiss  the  subject  of  maximums,  I  think  it 
best  to  consider,  whether  this  doctrine  will  apply  to  the 
motion  of  the  overshot  wheels.  It  seems  to  be  the  ge- 
neral opinion  of  those,  who  consider  the  matter,  that  it 
will  not ;  but,  that  the  slower  the  wheel  moves,  provided 
it  be  capacious  enough  to  hold  all  the  water,  without 
losing  any  imtil  it  be  delivered  at  the  bottom  of  the 
wheel,  the  greater  will  be  the  effect,  which  appears  to 
be  the  case  in  theory  (see  art.  36) ;  but  how  far  this 
theory  will  hold  good  in  practice  is  to  be  considered. 
Having  met  with  the  ingenious  James  Smeaton's  expe- 
riments, where  he  shews,  that,  when  the  circumference 
of  his  little  M'heel,  of  24  inches  diameter,  (head  6  inches) 
moved  with  about  3,1  feet  per  second  (although  the 
greatest  effect  was  diminished  about  J^  of  the  whole)  he 
obtained  the  best  effect,  with  a  steady,  regular  motion. 
Hence  he  concludes  about  three  feet  to  be  the  best  ve- 
locity for  the  circumference  of  overshot  mills.  See  art. 
68.  I  undertook  to  compare  this  theory  of  his,  with  the 
best  mills  in  practice,  and,  finding  that  those  of  about  17 
feet  diameter,  generally  moved  about  9  feet  per  second, 
being  treble  the  velocity  assigned  by  Smeaton,  I  be- 
gan to  doulDt  the  theory,  which  led  me  to  inquire  into 
the  principle  that  moves  an  overshot  wheel,  and  this 'I 


Chap,  11.]  MECHANICS.  75 

found  to  be  a  body  descending  by  its  gravity,  and  sub- 
ject to  all  the  laws  of  falling  bodies,  (art.  9)  or  bodies  of 
descending  inclined  planes,  and  curved  surfaces  (art. 
10,  11,)  the  motion  being  equably  accelerated  in  the 
whole  of  its  descent,  its  velocity  being  as  the  square  root 
of  the  distance  descended  through,  and  the  diameter  of 
the  wheel  Avas  the  distance  the  water  descended  through. 
From  thence  I  concluded,  that  the  velocity  of  the  cir- 
cumferance  of  the  overshot  wheels,  was  as  the  square 
root  of  their  diameters,  and  of  the  distance  the  water  has 
to  descend,  if  it  be  a  breast  or  pitch-back  wheel :  then, 
taking  Smeaton's  experiments,  with  his  wheel  of  2  feet 
diameter,  for  a  foundation,  I  say.  As  the  square  root  of 
the  diameter  of  Smeaton's  wheel,  is  to  its  maximum  ve- 
locity, so  is  the  square  root  of  the  diameter  of  any  other 
wheel,  to  its  maximum  velocity.  Upon  these  principles 
I  have  calculated  the  following  table  ;  and,  having  com- 
pared it  with  at  least  50  mills  in  practice,  found  it  to  agree 
so  nearly  with  all  the  best  constructed  ones,  that  I  have 
reason  to  believe  it  is  founded  on  true  principles. 

If  an  overshot  wheel  moves  freely  without  resistance, 
it  will  require  a  mean  velocity,  between  that  of  the  wa- 
ter coming  on  the  wheel,  and  the  greatest  velocity  it 
would  acquire,  by  falling  freely  through  its  whole  de- 
scent :  therefore  this  mean  velocity  will  be  greater,  than 
tlie  velocity  of  the  water  coming  on  the  wheel ;  conse- 
quently the  backs  of  the  buckets  will  overtake  the  wa- 
ter, and  drive  a  great  part  of  it  out  of  the  wheel.  But, 
the  velocity  of  the  water  being  accelerated  by  its  gravi- 
ty, overtakes  the  wheel,  perhaps  half  way  down,  and 
presses  on  the  buckets,  until  it  leaves  the  wheel :  there- 
fore the  water  presses  harder  upon  the  buckets  in  the 
lower,  than  in  the  upper  quarter  of  the  wheel.  Hence 
appears  the  reason  why  some  wheels  cast  their  water, 
which  is  always  the  case,  when  the  head  is  not  suffi- 
cient to  give  it  velocity  enough  to  enter  the  buckets. 
But  this  depends  also  much  on  the  position  of  the 
buckets,  and  direction  of  the  shute  into  them.  It,  how- 
ever, appears  evident  that  the  head  of  water  above  the 
wheel,  should  be  nicely  adjusted,  to  suit  the  velocity  of 


76  MECHANICS.  [Chap.  II 

the  wheel.  Here  we  may  consider,  that  the  head  above 
the  wheel  acts  by  percussion,  or  on  the  same  principles 
with  the  undershot  wheel,  and,  as  we  have  shewn  (art. 
41.)  that  the  undershot  wheel  should  move  with  nearly 
2-3  of  the  velocity  of  the  water,  it  appears,  that  we 
should  allow  a  head  over  the  wheel,  that  will  give  such 
velocity  to  the  water,  as  will  be  to  that  of  the  wheel  as  3 
to  2.  Thus  the  whole  descent  of  the  water  of  a  mill- 
seat  should  be  nicely  divided,  between  head  and  fall,  to 
suit  each  other,  in  order  to  obtain  the  best  effect,  and  a 
steady-moving  mill.  First  find  the  velocity  that  the 
wheel  will  move  with,  by  the  weight  of  the  water,  for 
any  diameter  you  may  suppose  you  will  take  for  the 
wheel,  and  divide  said  velocity  into  two  parts  ;  then  try 
if  your  head  is  such,  as  will  cause  the  water  to  come  on 
with  a  velocity  of  3  such  parts,  making  due  allowances 
for  the  friction  of  the  water,  according  to  the  aperture. 
See  art.  55.  Then  if  the  buckets  and  direction  of  the 
shute  be  right,  the  wheel  will  receive  the  water  well,  and 
move  to  the  best  advantage,  keeping  a  steady,  regular 
motion  when  at  work,  loaded  or  charged  with  a  resistance 
equal  to  2-3  of  its  power,  (art.  41,  42.) 


Chap.  11.] 


MECHANICS. 


71 


A  TABLE 


VELOCITIES  OF  THE  CIRCUMFERENCE 


OVERSHOT  WHEELS, 

Suitable  to  their  Diameters,  or  rather  to  the  Fall,  after  the  Water  strikes 
the  Wheel ;  and  of  the  head  of  Water  above  the  Wheel,  suitable  to  said 
Velocities,  also  of  the  Number  of  Revolutions  the  Wheel  will  perform  iji 
a  Mmute,  when  rightly  charged 


o 

^ 

K 

> 

!25 

p 

3 
n 

n 

-i 
o 

-*> 

5* 

0  =  0^ 

=•  _" 

•    r>  ^ 

'*  0 

-  ? 

,-   ^   D. 

els- 

0 

P 

P' 

p 

it 

1  c 

s; 

2. 

0 

1^^ 

^^g- 

m  _  < 

0 

3  5- 
1- 

5' 

a' 

n 

^  '^ « 

0  ~, 

3     M     0 

•    ^  3 
7  01 

-» 
• 

n  0 

2 

3,1 

3 

3.78 

4 

4,38 

5 

4,88 

6 

5,36 

7 

5,  8 

8 

6,19 

9 

6,57 

1,41 

,1 

1,51 

14,3 

10 

6,92 

1,64 

,1 

1,74 

13, 

11 

7,24 

1,84 

,1 

1,94 

12,6 

12 

7,57 

2, 

.2 

2,2 

12, 

13 

7,86 

2,17 

2,47 

1154 

14 

8,19 

2,34 

,4 

2,74 

11.17 

15 

8,47 

2,49 

,5 

2,99 

10,78 

15 

8,76 

2,68 

,6 

3,28 

10,4 

17 

9. 

2,  8 

,7 

3,5 

10,1 

18 

9,28 

3, 

,8 

r»  0 
0,0 

9,8 

19 

9,  5 

3,13 

,9 

4,03 

9,54 

20 

9,78 

3,34 

1, 

4,34 

9,3 

21 

10, 

3,49 

1.05 

4,54 

*M 

22 

10,28 

3,76 

1,1 

4,86 

8,9 

23 

10,  5 

3  84 

1,15 

4.99 

8.7 

24 

10,  7 

4,97 

1,2 

5,27 

8,5 

25 

10,95 

4,  2 

1,25 

'5,45 

8,3 

26 

11,16 

4,27 

1,3 

5,57 

8,19 

27 

11,36 

4,42 

1,35 

5,77 

8,03 

28 

11.54 

4,56 

3,4 

5,96 

7,93 

29 

11,78 

4,  7 

1,45 

615 

7,75 

30 

11,99 

4,  9 

15 

6,4 

7,63 

78  MECHANICS.  [Chap.  11. 

This  doctrine  of  maximums  is  very  interesting,  and 
is  to  be  met  with  in  many  occurences  through  life. 

1.  It  has  been  shewn,  that  there  is  a  maximum  load 
and  velocit}'  for  all  engines,  to  suit  the  power  and  velo- 
city of  the  moving  power. 

2.  There  is  also  a  maximum  size,  velocity,  and  feed 
for  mill-stones,  to  suit  the  power ;  and  velocity  for  roll- 
ing screens,  and  bolting-reels,  by  which  the  greatest 
work  can  be  done  in  the  best  manner,  in  a  given  time. 

3.  A  maximum  degree  of  perfection  and  closeness, 
with  which  grain  is  to  be  manufactured  into  flour,  so  as 
to  yield  the  greatest  profit  by  the  mill  in  a  day  or  week, 
and  this  maximum  is  continually  changing  with  the 
prices  in  the  market,  so  that  what  would  be  the  greatest 
profit  at  one  time,  will  sink  money  at  another.  See 
art.  113. 

4.  A  maximum  weight  for  mallets,  axes,  sledges,  &c. 
according  to  the  strength  of  those  that  use  them. 

A  true  attention  to  the  principles  of  maximums,  will 
prevent  us  from  runnmg  into  many  errors. 


Ghap.l2.]  HYDRAULICS,  79 


CHAPTER  XII. 


HYDRAULICS. 

UNDER  the  head  of  Hydraulics  we  shall  only  consi- 
der such  parts  of  this  science,  as  immediately  relate  to 
our  purpose,  viz.  such  as  may  lead  to  the  better  under- 
standing of  the  principles  and  powers  of  water,  acting  on 
mill-wheels,  and  conveying  water  to  them. 


ART.   45. 

OP  SPOUTING  FLUIDS. 

%)outing  fluids  observe  the  following  laws  : 

1.  Their  velocities  and  powers,  under  equal  pressures, 
or  equal  perpendicular  heights,  and  equal  apertures,  are 
equal  in  all  cases.* 

2.  Their  velocities  imder  different  pressures  or  per- 
pendicular heights,  are  as  the  square  roots  of  those  pres- 
sures or  heights ;  and  their  perpendicular  heights  or 
pressures,  are  as  the  squares  of  their  velocities. f 

•  It  makes  no  difference  whether  the  water  stands  perpendicular  above 
the  aperture,  or  incliningly  (see  plate  III,  fig.  22)  providing  the  perpendi- 
cular height  be  the  same  ;  or  whether  the  quantity  be  great  or  small,  pro- 
viding it  be  sufficient  to  keep  up  the  fluid  to  the  same  height. 

t  This  law  is  similar  to  the  4th  law  of  falling  bodies,  their  velocities 
being  as  the  square  root  of  their  spaces  passed  through  ;  and  by  experi- 
ment it  is  known,  that  water  will  spoilt  from  under  a  4  feet  head,  16,2  feet 
per  second,  and  from  under  a  16  feet  head,  32,4  feet  per  second,  and  from 
under  a  16  feet  head,  32,4  feet  per  second,  which  is  only  double  to  that  of 
a  4  feet  head,  although  there  be  a  quadruple  pressure.  Therefore  by  this 
law  we  can  find  the  velocity  of  water  spou'ing  from  under  any  given  head  ; 
for  as  the  square  root  of  4  equal  2  is  to  16,2  its  velocity,  so  is  the  square 
root  of  16  equal  4,  to  32,4  squared,  to  16  its  head  :  by  which  ratio  we  cna 
find  the  head  that  will  produce  any  velocity. 


80  HYDRAULICS.  [Chap.  12. 

3.  Their  quantities  expended  through  equal  apertures, 
in  equal  times,  under  unequal  pressures,  are  as  their  ve- 
locities simply.* 

4.  Their  pressures  or  heights  being  the  same,  their 
effects  are  as  their  quantities  expended.f 

5.  Their  quantities  expended  being  the  same,  their 
effects  are  as  their  pressure,  or  heighi  of  their  head  di- 
rectly.| 

6.  Their  instant  forces  with  equal  apertures,  are  as 
the  squares  of  their  velocities,  or  as  the  height  of  their 
heads  directly. 

7.  Their  effects  are  as  their  quantities,  multiplied  into 
the  squares  of  their  velocities.  § 

*  It  is  evident  that  a  double  velocity  will  vent  a  double  quantity. 

f  If  the  pressure  be  equal,  the  velocity  must  be  eq  al ;  and  it  is  evident, 
that  double  quantity,  witheqial  velocity  will  produce  a  double  effect. 

i  That  is,  if  we  suppose  16  cubic  feet  of  water  to  issue  from  under  n  4 
feet  head  in  a  second,  and  an  equal  quantity  to  issue  in  the  same  time 
from  under  16  feet  head,  then  'heir  effects  will  be  as  4 to  16.  But  we  must 
note,  that  the  aperture  in  the  last  case  must  be  only  half  of  'hat  in  the  first, 
as  the  velocity  will  be  double. 

§  This  is  evident  from  this  consideration,  viz.  that  a  quadruple  impulse 
is  required  to  produce  a  double  velocity,  by  law  2nd,  wlitre  ihe  velocities 
are  as  the  square  roots  of  their  heads  :  therefore  their  effects  must  be  as 
the  squares  of  their  velocities- 


ART.  46. 


DEMONSTRATION. 


Let  A  F,  (plate  III,  fig'.  26)  represent  a  head  of  water  16  feet  high,  and 
suppose  it  divided  into  4  different  heads  of  4  feet  each,  as  B  C  D  E;  ihea 
suppose  we  draw  a  gate  of  1  foot  square  at  each  head  successively,  always 
sinking  the  water  in  the  head,  so  that  it  will  be  but  4  feet  above  the  centre 
of  the  gate  in  each  case. 

Now  it  is  known  that  the  velocity  under  a  four  feet  head,  is  16,2  feet  per 
second;  say  16  feet  to  avoid  fractions,  which  will  issue  16  cubic  feet  of 
water  per  second,  and  for  sake  of  round  numbers,  let  unity  or  1  represent 
the  quantity  of  a  cubic  foot  of  water ;  then,  by  the  7th  lav  the  effec  will  be 
as  the  quantity  multiplied  by  the  square  of  the  velocity  ;  that  is,  16  mulii- 
plied  by  16  is  equal  to  256,  which  multiplied  by  16,  the  quantity  is  equal 
to  4096,  the  effect  of  each  4  feet  head ;  and  4096  multiplied  by  4  is  eq  al 
to  16384,  for  the  sum  of  effects,  of  all  the  4  feet  heads. 

Then  as  the  velocity  under  a  16  feet  head  is  32,4  feet,  say  32  to  avoid 
fractions  ;  the  gate  must  be  drawn  to  only  half  the  sizp,  to  vend  the  16  'u- 
bic  feet  of  water  per  second  as  before  (because  the  velocity  is  double);  ,iitn, 
to  find  the  effect,  32  multiplied  by  32,  is  equal  to  1024;"which  mnltipl  ed 
by  16,  the  quantity,  gives  the  effect,  16384,  equal  the  sum  of  all  the  4  teet 


Chap.  12.]  HYDRAULICS.  8t 

head  which  ag^rees  with  the  practice  and  experience  of  the  best  teachers. 
But  if  their  effects  were  as  their  velocities  simply,  then  the  effect  of  each  4 
feet  head  would  be,  16  multiplied  by  16,  equal  to  256 ;  which,  multiplied 
by  4,  is  equal  to  1024,  for  tlie  sum  of  the  eJlects  of  all  the  4  feet  heads; 
and  16  multiplied  by  32  equal  to  512,  for  the  effect  of  the  16  feet  head, 
which  is  only  half  of  the  effect  of  the  same  head  when  divided  into  4  partsj 
which  is  contrary  to  both  experiment  and  reason. 

Again,  let  us  suppose  tlie  body  A  of  quantity  16,  to  be  perfectly  elastic, 
to  fall  16  feet  and  strike  V,  a  perfect  el.isiic  plane,  it  will  (by  laws  of  fall- 
ing bodies)  strike  with  a  velocity  of  32  feet  per  second,  and  rise  16  feet 
to  A  again. 

B<it  if  it  fall  only  to  B,  4  feet,  it  will  strike  with  16  feet  per  second,  and 
rise  4  feet  to  A  ag-ain.  Here  the  effect  of  the  16  feet  fall  is  4  times  the 
effect  of  the  4  feet  fall,  because  the  body  rises  4  times  the  height. 

But  if  we  count  the  effective  momentum  of  their  strokes  to  be  as  their 
velocities  simply,  then  16  multiplied  by  32  is  equal  to  512,  the  momentum 
of  the  16  feet  fall;  and  16  multiplied  by  16  is  equal  to  256;  which,  multi- 
plied by  4,  IS  equal  to  1024,  for  the  sum  of  the  momentums  of  the  strokes 
of  16  feet  divided  into  4  equal  falls,  which  is  absurd.  But  if  we  count  their 
momentums  to  be  as  the  squares  of  their  velocities,  the  effects  will  be 
equal. 

Again,  it  is  evident  that  whatever  impulse  or  force  is  required  to  give  a 
body  a  velocity,  the  same  force  or  resistance  will  be  required  to  stop  it; 
therefore,  if  the  impulse  be  as  the  square  of  the  velocity  produced,  the 
force  or  resistance  will  be  as  the  squares  of  the  velocity  also.  But  the  im- 
pulse is  as  the  sqnares  of  the  velocity  produced,  which  is  evident  from  this 
consideration,  Sfippose  we  place  a  light  body  at  the  gate  B,  of  4  feet  head, 
and  pressed  with  4  feet  of  water ;  when  the  gate  is  drawn  it  will  fly  off" 
with  a  velocity  of  16  feet  per  second  ;  and  if  we  increase  the  head  to  16 
feet,  it  will  fly  off  with  32  feet  per  second.  Then,  as  the  square  of  16  equal 
to  256  is  to  the  square  of  32  equal  to  1024,  so  is  4  to  16.     Q.  E.  D. 

ART.    47. 

To  compare  this  7th  law  with  the  theory  of  undershot  mills,  established 
art.  42,  where  it  is  shewn  that  the  power  is  to  the  effect  as  3  to  1 ;  then, 
by  the  7th  law,  the  quantity  shewn  by  the  scale,  plate  II,  to  be  32,4  mul- 
tiplied by  1049,76  the  square  of  the  velocity,  which  is  equal  to  3401,2124, 
the  effect  of  the  16  feet  head  ;  then,  for  the  effect  of  a  4  feet  head,  with 
equal  aperture  quantity,  by  scale,  16,2  multiplied  by  262,44.  the  velocity- 
squared,  is  equal  to  425,1528,  the  effect  of  a  four  feet  head  ;  here  the  ratio 
of  the  effects  are  as  8  to  1. 

Then,  by  the  theory,  which  shews  that  an  undershot  wheel  will  hoist 
1-3  of  the  water  that  turns  it,  to  the  whole  height  from  which  it  descended, 
the  1-3  of  32,4  the  quantity,  being  equal  to  10,8  multiplied  by  16,  perpen- 
dicular ascent,  which  is  equal  to  172,8,  effect  of  a  16  feet  head  :  and  1  3  of 
16,2  quantity,  whicii  is  equal  to  5,4  multiplied  by  4,  perpendicular  ascent, 
IS  equal  to  21,6  effect  of  4  feet  head,  by  the  theory:  and  here  again  the 
ratio  of  the  effects  are  as  8  to  1 ;  and, 

as  3401,2124,  the  eff.  ct  of  16  feet  head, 7  .     ,.,.  , 

is  to  425,1528,  the  effect  of  4  feet  head,5 ''^  ^'^'^ '*"'' 

so  is  172,8  the  effect  of  6  feet  head, 7  .     .,     ,. 

to  21,6  the  effect  of  4  feet  head,     $  ^y  ^''*  *^^°'>'- 
The  quantities  being  equal,  their  effects  are  as  the  height  of  their  heads 
direcily,as  by5ih  law,  and  as  the  squ -res  of  their  velocities  as  by  7th  law. 
He.jce  It  appears,  that  the  theory  agrees  with  the  established  laws,  which 
I  take  to  be  a  confirmation  that  it  is  well  founded. 


82 


HYDRAULICS. 


[Chap.  12. 


8.  Therefore  their  effects  or  powers  with  equal  aper- 
tures, are  as  the  cubes  of  their  velocities.*^ 

9.  Their  velocity  under  any  head  is  equal  to  the  velo- 
city that  a  heavy  body  would  acquire  in  falling  from  the 
same  height. | 

10.  Their  velocity  is  such  under  any  head  or  height,  as 
will  pass  over  a  distance  equal  to  twice  the  height  of  the 
head,  in  a  horizontal  direction,  in  the  time  that  a  heavy 
body  falls  the  distance  of  the  height  of  the  head. 

11.  Their  action  and  re-action  are  equal. ^ 

12.  Their  being  non-elastic,  communicate  only  half 
their  real  force  by  impulse,  in  striking  obstacles ;  but  by 

*  The  effects  of  striking  fluids  with  equal  apertures  are  as  the  cubes  of 
their  velocities,  for  the  following  reusons,  viz.  1st.  If  an  equal  quantity  strike 
with  double  velocity,  the  effect  is  quadruple  on  that  account  by  the  7th 
law;  and  a  double  velocity  expends  a  double  quantity  by  3d  law;  there- 
fore, the  effect  is  amounted  to  the  cube  of  the  velocity. — The  theory  for 
undershot  wheels  agrees  with  this  law  also. 


A  SCALE 

Founded  on  the  3d,  6th  and  7th  laws,  shewing  the  effects  of  striking  Fluids, 
with  different  Velocities. 


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i  The  falling  body  is  acted  on  by  the  whole  force  of  its  own  gravity,  in 
the  whole  of  its  descent  through  any  space  ;  and  the  whole  sum  of  this  ac- 
tion that  is  acquired  as  it  arrives  at  the  lowest  point  of  its  fall,  is  equal  to 
the  pressure  of  the  whole  head  or  perpendicular  height  above  the  issue  : 
therefore  their  velocities  are  equal. 

%  That  is,  they  re-act  back  against  the  penstock  with  the  same  force  that 
it  issues  against  the  obstacle  it  strikes;  this  is  the  principle  by  which  Bar- 
ker's mills,  and  all  those  that  are  improvements  thereon,  move- 


K 


thap.  12.]  HYDRAULICS.  83 

their  gravity  produce  effects,  equal  to  elastic  or  solid 
bodies.* 


.IppUcatwn  of  the  Laws  of  Motion  to  Undershot  JVheels. 

To  give  a  short  and  comprehensive  detail  of  the  ideas 
I  have  collected  from  the  different  authors,  and  from  the 
result  of  my  own  reasoning  on  the  laws  of  motion,  and 
of  spouting  fluids,  as  they  apply  to  move  undershot  mills, 
I  constructed  fig.  44,  plate  V. 

Let  us  suppose  two  large  wheels,  one  of  12  feet,  and 
the  other  of  24  feet  radius,  then  the  circumference  of 
the  largest,  will  be  double  that  of  the  smallest :  and  let 
A  16,  and  C  16,  be  two  penstocks  of  water,  of  16  feet 
head,  each. 

1.  Then,  if  we  open  a  gate  of  1  square  foot  at  4,  to 
issue  from  the  penstock  A  16,  and  impinge  on  the  small 
wheel  at  I,  the  water  being  pressed  by  4  feet  head,  ^vill 
move  16  feet  per  second,  (we  omit  fractions.)  The  in- 
stant pressure  or  force  on  that  gate,  being  four  cubic 
feet  of  water,  it  will  require  a  resistance  of  4  cubic  feet 
of  water,  from  the  head  C  16  to  stop  it,  and  hold  it  in 
equilibrio,  (but  we  suppose  the  water  cannot  escape  un- 
less the  wheel  moves,  so  that  no  force  be  lost  by  non- 
elasticity.)  Here  equal  quantities  of  matter,  with  equal 
velocities,  have  their  momentums  equal. 

2.  Again,  suppose  we  open  a  gate  of  1  square  foot  at 
A  16  under  16  feet  head,  it  will  strike  the  large  wheel 
at  k,  with  velocity  32,  its  instant  force  or  pressure  being 
16  cubic  feet  of  water,  it  will  require  16  cubic  feet  re- 
sistance, from  the  head  C  16,  to  stop  or  balance  it.  1\\ 
this  case  the  pressure  or  instant  force  is  quadruple,  and 
so  is  the  resistance,  but  the  velocity  only  double,  to  the 
first  case.     In  these  two  cases,  the  forces  and  resistances 

•  When  non-elastic  bodies  strike  an  obstacle,  one  half  of  their  force  is 
spent  in  a  lateral  direction,  in  changing'  their  figure,  or  in  splashing  about. 
See  art.  8. 

For  want  of  due  consideration  or  knowledge  of  this  principle,  many  have 
been  the  errors  committed  by  applying  water  to  act  by  impulse,  when  it 
would  have  produced  a  double  effect  by  its  gravity. 


84  HYDRAULICS.  [Chap  12. 

being  equal  quantities,  with  equal  velocities,  their  mo- 
mentums  are  equal. 

3.  Again,  suppose  the  head  C  16  to  be  raised  to  E,  16 
feet  above  4,  and  a  gate  draw  n  -}  of  a  square  foot,  then 
the  instant  pressure  on  the  float  I  of  the  small  wheel, 
will  be  4  cubic  feet,  pressing  on  |  of  a  square  foot,  and 
"will  exactly  balance  4  cubic  feet,  pressing  on  1  square 
foot,  from  the  head  A  16 ;  and  the  wheel  will  be  in 
equilibrio,  (supposing  the  water  cannot  escape  until  the 
■wheel  moves  as  before),  although  the  one  has  power  of 
velocity  32,  and  the  other  only  16  feet  per  second. 
Their  loads  at  equilibrio  are  equal,  consequendy  their 
loads  at  a  maximum  velocity  and  charge,  will  be  equal, 
but  their  velocities  different. 

Then,  to  try  their  effects,  suppose,  first,  the  wheel  to 
move  by  the  4  feet  head,  its  maximum  velocity  to  be 
half  the  velocity  of  the  water,  which  is  16,  and  its  maxi- 
mum load  to  half  its  greatest  load,  which  is  4,  by  Wa- 
ring's  theor}- ;  then  the  velocity  16  |  2>cby  the  load 
4  I  2=16,  the  effect  of  the  4  feet  head,  with  16  cubic 
feet  expended;  because  the  velocity  of  the  water  is  16, 
and  the  gate  1  foot. 

Again,  suppose  it  to  move  by  the  16  feet  head  and 
gate  of  I  of  a  foot ;  then  the  velocity  32  |  2xby  the 
load  4  (  2=3S,  the  effect,  with  but  8  cubic  feet  expend- 
ed, because  the  velocity  of  the  water  is  32,  and  the  gate 
but  I  of  a  foot. 

In  this  case  the  instant  forces  are  equal,  each  being 
4;  but  the  one  moving  a  body  only  I  as  heavy  as  the 
other,  moves  with  velocity  32,  and  produces  effect  32, 
while  the  other,  moving  with  velocity  16,  produces  effect 
16.  A  double  velocity,  with  equal  instant  pressure, 
produces  a  double  effect,  which  seems  to  be  according 
to  the  Newtonian  theory.  And  in  this  sense  the  mo- 
mentums  of  bodies  in  motion  are  as  their  quantities, 
multiplied  into  their  simple  velocities,  and  this  I  call  the 
instant  momentums. 

But  when  we  consider,  that  in  the  above  case  it  was 
the  quantity  of  matter  put  in  motion,  or  water  expended, 
that  produced  the  effect,  we  find  that  the  quantity  16, 
with  velocity  16,  produced  effect  16;   while  qu.  8,  with 


Chap.  12.]  HYDRAULICS.  85 

velocity  32,  produced  effect  32.  Here  the  effects  are  as 
their  quantities,  niultiphed  into  the  squares  of  their 
velocities ;  and  this  I  call  the  effective  momentums. 

Again,  if  the  quantity  expended  under  each  head,  had 
been  equal,  their  effects  would  have  been  16  and  64, 
which  is  as  the  squares  of  their  velocities,  16  and  32. 

4.  Again,  suppose  both  wheels  to  be  on  one  shaft, 
and  let  a  gate  of  1-8  of  a  square  foot  be  drawn  at  16  C, 
to  strike  the  wheel  at  k,  the  head  being  16  feet,  the  in- 
stant pressure  on  the  gate  will  be  2  cubic  feet  of  water, 
which  is  half  of  the  4  feet  head  with  1  foot  gate,  from  A 
4  striking  at  I ;  but  the  16  feet  head,  with  instant  pres- 
sure 2,  acting  on  the  great  wheel,  will  balance  4  feet  on 
the  small  one,  because  the  lever  is  of  double  length, 
and  the  wheels  will  be  in  equilibrio.  Then,  by  Waring's 
theory,  the  greatest  load  of  the  16  feet  head  being  2, 
its  load  at  a  maximum  will  be  1,  and  the  velocity  of  the 
water  being  32,  the  maximum  velocity  of  the  wheel  will 
be  16.  Now  the  velocity  16x1=16,  the  effect  of  the  16 
feet  head,  and  gate  of  1-8  of  a  foot.  The  greatest  load 
of  the  4  feet  head  being  4,  its  maximum  load  2,  the  ve- 
locity of  the  water  16,  and  the  velocity  of  the  wheel  8, 
now  8x2=16,  the  effect.  Here  the  effects  are  equal: 
and  here  again  the  effects  are  as  the  instant  pressures, 
multiplied  into  their  simi)le  velocities :  and  the  resistances 
that  would  instantly  stop  them,  must  be  equal  thereto,  in 
the  same  ratio. 

But  v\hen  we  consider,  that  in  this  case  the  4  feet 
head  expended  16  cubic  feet  of  water,  with  velocity  16, 
and  produced  effect  16;  while  the  16  feet  head  expended 
only  -l  cubic  feet  of  water,  with  velocity  32,  and  produced 
effect  16,  we  find,  that  the  effects  are  as  their  quantities, 
multiplied  into  the  squares  of  their  velocities. 

And  when  we  consider,  that  the  gate  of  1-8  of  a  square 
foot,  with  velocity  32,  produced  effects  equal  to  the  gate 
of  1  square  foot,  with  velocity  16,  it  is  evident,  that  if 
we  make  the  gates  equal,  the  effects  will  be  as  8  to  1 ; 
that  is,  the  effects  of  spouting  fluids,  with  equal  apertures, 
are  as  the  cubes  of  their  velocities ;  because,  their  instant 
forces  are  as  the  squares  of  their  velocities  by  6th  law, 
although  the  instant  force  of  solids  are  as  their  velocities, 


86  HYDRAULICS.  [Chap.  12. 

simply,  and  their  eiFects  as  the  squares  of  their  velocities, 
a  double  velocity  does  not  double  the  quantity  of  a  solid 
body  to  strike  in  the  same  time. 


ART.  48. 
THE  HYDROSTATIC  PARADOX. 

The  pressure  of  fluids  is  as  their  perpendicular 
heights,  without  any  regard  to  their  (juantity :  and  their 
pressure  upwards  is  equal  to  their  pressure  downwards. 
In  short,  their  pressure  is  every  way  equal,  at  any  equal 
distance  f^om  their  surface.* 

•  To  explain  whicl»,  let  A  B  C  D,  plate  III,  fig.  22.  be  a  vessel  of  water  of 
a  Ci'bical  form,  with  a  small  lube  as  H,  fixed  there  n;  let  a  hole  of  the  same 
size  of  the  tube  be  made  at  o,  and  covered  wiih  a  piece  of  pliant  leather, 
nailed  ll>ereon,  so  as  to  hold  the  water.  Then  fill  the  vessel  with  water  by 
the  tube  H,  and  it  will  press  upwards  agamst  the  leather,  and  raise  it  in  a 
convex  form,  requiring  just  as  much  weight  to  press  it  dou  n,  as  will  be 
equal  to  the  weight  of  water  in  the  tube  H.  Or  if  we  set  a  glass  tube  over 
the  hole  at  o,  and  pour  water  therein,  we  will  find  tliat  the  water  in  the 
tube  o,  nr.ust  be  of  the  same  lieight  of  that  in  the  tube  H,  beibre  the  leather 
ffill  subside,  even  if  the  tube  O  be  much  larger  than  H;  w-hicli  shews,  that 
the  pressHre  upwards  is  equal  to  the  pressure  downwards;  because  the 
water  pressed  up  against  the  leather  with  the  whole  weiglit  of  the  water  in 
the  tube  H.  Again,  if  we  fill  'he  vessel  by  the  tube  I,  it  will  rise  to  the 
same  height  in  H  that  it  is  in  I;  the  pressure  being  the  same  in  every  part 
of  the  vessel  as  if  it  had  been  filled  by  H  ;  and  the  pressure  on  the  bottom 
of  the  vessel  will  be  the  same,  whether  the  tube  H  be  of  the  whole  size  of 
the  vessel,  or  only  one  quarter  of  an  inch  diameter.  For  suppose  H  to  be 
1-4  of  an  inch  diameter,  and  the  whole  top  of  the  vessel  of  leather  as  at  o, 
Hnd  we  powr  water  down  H,  it  will  press  the  leather  up  with  such  force, 
that  it  will  require  a  column  of  water  of  the  whole  size  of  the  vessel,  and 
height  of  H,  to  cause  the  leather  to  subside.     Q.  E.  D. 

ART.    49. 

And  again,  suppose  we  make  two  holes  in  the  vessel,  one  close  to  the 
bottom,  and  the  other  in  the  bottom,  both  of  one  size,  the  water  will  issue 
with  equal  velociiy  out  of  each;  which  may  be  proved  by  holding  equal 
vessels  under  each,  which  will  be  filled  in  equal  time;  which  shews,  that 
the  pressure  on  the  sides  and  bottom  are  equal  under  equal  distances  fi'om 
the  surface.  And  this  velocity  will  be  the  same  whether  the  tube  be  filled 
by  pipe  1,  or  H,  or  by  a  tube  the  whole  size  of  the  vessel,  provided  the 
perpendicular  height  be  equal  in  all  cases. 

From  what  has  been  said,  it  appears,  that  it  makes  no  difference  in  the 
power  of  water  on  mill-wheels,  whether  it  be  brought  on  in  an  open  fore- 
bay  and  perpetidicular  penstock,  or  down  an  inclining  one,  as  I  C  ;  or  under 
ground  in  a  close  trunk,  in  any  form  that  may  best  suit  the  situation  and 


€hap.  12.]  HYDRAULICS.  87 

In  a  vessel  of  cubic  form,  whose  sides  and  bottom  are 
equal,  the  pressure  on  each  side  is  just  half  the  pressure 
on  the  bottom ;  therefore  the  pressure  on  the  bottom  and 
sides,  is  equal  to  three  times  the  pressure  on  the  bottom,* 

And  in  this  sense  fluids  may  be  said  to  act,  with  three 
times  the  force  of  solids.  Solids  act  by  gravity  only,  but 
fluids  by  gravity  and  pressure  jointly.  Solids  act  with  a 
force  proportional  to  their  quantity  of  matter ;  but  fluids 
act  with  a  pressure  proportional  to  their  altitude  only. 


ART.    50. 

The  weight  of  a  cubic  foot  of  water  is  found  by  ex- 
perience, to  be  1000  ounces  avoirdupoise,  or  62,5Ib. 
On  these  priciples  is  founded  the  following 

THEOREM. 

The  area  of  the  base  or  bottom,  or  any  part  of  a  ves- 
sel, of  whatever  form,  multiplied  by  the  greatest  perpen- 
dicular height  of  any  part  of  the  fluid,  above  the  centre 
of  the  base  or  bottom,  whatever  be  its  position  with  the 
horizon,  produces  the  pressure  on  the  bottom  of  said 
vessel. 

PROBLEM  L 

Given,  the  length  of  the  sides  of  the  cubic  vessel  (fig. 
22,  pi.  III.)  6  feet  required  the  pressure  on  the  bottom 
when  full  of  water. 

Then  6x6=36  feet  the  area,  multiplied  by  6,  the  al- 
titude,=216,  the  quantity  or  cubic  feet  of  water,  press- 
ing on  the  bottom  ;  which  multiplied  by  62,5= 135001b. 
the  whole  pressure  on  the  bottom- 
circumstances,  provided  that  tlie  trunk  be  large  enough  to  supply  the  water 
fast  enough  to  keep  the  head  from  sinking. 

This  principle  of  the  Hydrostatic  Paradox  has  sometimes  taken  place  m 
undershot  mills,  by  pressing  up  against  the  bottom  of  tiie  buckets,  tlitrebj 
destroyingorcounteractinggreat  part  of  the  force  of  impulse-  See  art.  53- 

*  For  demonstration,  see  Philosophia  P.ritannia 


8»  HYDRAULICS.  [Chap.  12. 

PROBLEM  IL 

Given,  the  height  of  a  penstock  of  water,  31,5  feet, 
and  its  dimensions  at  bottom  3  by  3  feet,  inside,  requir- 
ed the  pressure  on  3  feet  high  of  one  of  its  sides, 

Then,  3x3=9  the  area,  multipUed  by  30  feet,  the 
perpendicular  height  or  head  above  its  centre=270  cu- 
bic feet  of  water  pressing,  which  x62,5=.  16 8751b.  the 
pressure  on  one  yard  square,  which  shews  what  great 
strength  is  required,  to  hold  the  water  under  such  great 
heads. 


ART.    51. 

RULE  FOR  FINDING  THE  VELOCITY  OP  SPOUTING   WATER. 

By  experiments  it  has  been  found,  that  water  will 
spout  from  under  a  4  feet  head,  with  a  velocity  equal  to 
16,2  feet  per  second,  and  from  under  16  feet  head,  with 
a  velocity  equal  to  32,4  feet  per  second. 

On  these  experiments,  and  the  2nd  law  of  spouting 
fluids,  is  founded  the  following  theorem,  or  general  rule 
for  finding  the  velocity  of  water  under  any  given  head. 

THEOREM  IL 

As  the  square  root  of  a  four  feet  head  (=2)  is  to  16,2 
feet,  the  velocity  of  the  water,  spouting  under  it,  so  is  the 
square  root  of  any  other  head,  to  the  velocity  of  the  wa- 
ter spouting  under  it. 

PROBLEM  L 

Given,  the  head  of  water  16  feet,  required  the  velocity" 
of  water  spouting  under  it. 

Then,  as  the  square  root  of  4  (=2)  is  to  16,2,  so  is  the 
square  root  of  16,  (=4)  to  32,4,  the  velocity  of  the  wa- 
ter under  the  16  feet  head. 

PROBLEM  XL 

Given,  a  head  of  water  of  11  feet,  required  the  velocity 
of  water  spouting  under  it. 


Ciiap.  12.]  HYDRAULICS.  89 

Then,  as  2: 16,2::  3,316: 26,73  feet  per  second,  the 
velocity  required. 


ART.    52, 

From, the  laws  of  spouting  fluids,  theorems  I.  and  II. 
the  theory  for  finding  the  maximum  charge  and  velocity 
of  undershot  wheels,  (art.  42)  and  the  principle  of  non- 
elasticity,  is  deduced  the  following  theorem  for  finding 
the  eftect  of  any  gate,  drawn  under  any  given  head,  upon 
an  undershot  water-wheel. 

THEOREM  III. 

Find  by  theorem  I.  (art.  50^  the  instantaneous  pres- 
sure of  the  water,  which  is  the  load  at  equilibrio,  and  2-3 
thereof  is  the  maximum  load,  which,  multiplied  bv  ,577 
of  the  velocity  of  the  water,  under  the  given  head,  (found 
by  theorem  11.)  produces  the  effect. 

PROBLEM. 

Given,  the  head  16  feet,  gate  4  feet  wide,  ,25  of  a  foot 
drawn,  required  the  effect  of  an  undershot  wheel,  per 
second.  The  measure  of  the  effect  to  be  the  quantity, 
multiplied  into  its  distance  moved,  (velocity)  or  into  its 
perpendicular  ascent. 

Then  by  theorem  L  (art.  50)  4x,25=l  square  foot 
the  area  of  the  gate  x  16=  16  the  cubic  feet  pressing; 
but,  for  the  sake  of  round  numbers,  we  call  each  cubic 
foot  1,  and  although  32,4  cubic  feet  strike  the  wheel  per 
second,  yet,  on  account  of  non-elasticity,  only  16  cubic 
feet  is  the  load  at  equilibrio,  and  2-3  of  l6  is  10,666, 
the  maximum  load. 

Then,  by  theorem  II.  the  velocity  is  32,4,  ,577  of 
which  is=i8,71,  the  maximum  velocity  of  the  wheel 
X  10,66,  the  load=  199,4,  the  effect. 

This  agrees  with  Smeaton's  observations,  where  he 
says,  (art.  67)  "  It  is  somewhat  remarkable,  that  though 
the  velocity  of  the  wheel,  in  relation  to  the  velocity  of 
the  water,  turn  out  to  be  more  than  1-3,  yet  the  impulse 

M 


90  HYDRAULICS.  [Chap.  12. 

of  the  water,  in  case  of  the  maximum,  is  more  than 
double  of  uhat  is  assigned  by  theory  ;  that  is,  instead  of 
4-9  of  the  column,  it  is  nearly  equal  to  the  whole  co- 
lumn." Hence  I  conclude,  that  non-elasticity  does  not 
operate  so  much  against  this  application,  as  to  reduce 
the  load  to  be  less  than  2-3.  And  when  we  consider, 
that  32,4  cubic  feet  of  water,  or  a  column  32,4  feet  long, 
strike  the  wheel  while  it  moves  only  18,71  feet,  the  ve- 
locity of  the  wheel  being  to  the  veloci- y  of  the  water  as 
577  to  1000,  may  not  this  be  the  reason  why  the  load 
is  just  2-3  of  the  head,  which  brings  the  effect  to  be  just 
,38  (a  little  more  than  1-3  of  the  power.)  This  I  admit 
because  it  agrees  with  experiment,  although  it  be  difficult 
to  assigTi  the  true  reason  thereof.  See  annotation,  art.  -12. 
Therefore  ,577  the  velocity  of  the  water=  18,71,  .nul- 
tiplied  by  2-3  of  16,  the  whole  colum.n,  or  instantaneous 
pressure,  pressing  on  the  wheel — art.  50 — which  is  10,66, 
produces  199,4  the  effect.  This  appears  to  be  the  true 
effect,  and  if  so,  the  true  theorem  will  be  as  follows, 
viz. 

THEOREM. 

Find,  by  theorem  I.  art.  50,  the  instantaneous  pres- 
sure of  the  water,  and  take  2-3  for  the  maximum  load; 
multiply  by  ,577  of  the  velocity  of  the  water — which  is 
the  velocity  of  the  wheel — and  the  product  will  be  the 
effect. 

Then  16  cubic  feet,  the  column,  multiplied  by  2-3= 
10,66,  the  load  which  multiplied  by  18,71  the  velocity 
of  the  wheel,  produces  199,4,  for  the  effect;  and  if  we 
try  different  heads  and  different  apertures,  we  find  the 
effects  to  bear  the  ratio  to  each  other,  that  is  agreeable 
to  the  laws  of  spouting  fluids. 


ART.    53. 
WATER  APPLIED  OX  WHEELS  TO  ACT  BY  GllAVITV. 

But  when  fluids  are  applied  to  act  on  wheels  to  pro- 
duce eflects  by  their  gravity,   they  act  on  very  different 


Chap.  12.]  HYDRAULICS.  91 

principles,  producing  double  effects,  to  what  they  do  by 
percussion,  and  then  their  powers  are  directly  as  their 
quantity  or  weight,  multiplied  into  their  perpendicular 
descent. 

DEMONSTRATION. 

Let  fig.  19,  plate  III.  be  a  lever,  turning  on  its  centre 
or  fulcrum  A.  Let  the  long  arm  A  B  represent  the 
perpendicular  descent,  16  feet,  the  short  arm"  A  D  a  de- 
scent of  4  feet,  and  suppose  water  to  issue  from  tiie 
trunk  F,  at  the  rate  of  50lb.  in  a  second,  falling  into  the 
buckets  fastened  to  the  lever  at  B.  Now,  from  the  prin- 
ciples of  the  lever — art.  16 — it  is.  evident,  that  50!b.  in  a 
second  at  B,  will  balance  2001b.  in  a  second,  at  D,  is- 
suing from  the  trunk  G,  on  the  short  arm ;  because 
50x16=4x200=800,  each.  Perhaps  it  may  appear 
plainer  if  we  suppose  the  perpendicular  line  or  diameter 
F  C,  to  represent  the  descent  of  16  feet,  and  the  diame- 
ter G  I  a  descent  of  4  feet.  By  the  laws  of  the  lever — 
art.  16 — it  is  shewn,  that,  to  multiply  50  into  its  perpen- 
dicular descent  16  feet  or  distance  moved,  is=200,  mul- 
tiplied into  its  perpendicular  descent  4  feet,  or  distance 
moved;  that  is,  50xl6=200x'i=800 ;  that  is,  their 
power  is  as  their  quantity,  multiplied  into  their  perpen- 
dicular descent ;  or  in  other  words,  a  fall  of  4  feet  u  ill 
require  4  times  as  much  water,  as  a  fall  of  1(5  feet,  to 
produce  equal  power  and  effects.     Q.  E.  D. 

Upon  these  principles  is  founded  the  following  simple 
theorem,  for  measuring  the  po^^■er  of  an  undershot  mill, 
or  of  a  quantity  of  water,  acting  upon  any  mill-wheel  by 
its  gravit}'. 

THEOREM  IV. 

Cause  the  water  to  pass  along  a  regular  canal,  and 
multiply  its  depth  in  feet  and  parts,  by  its  width  in  feet 
and  parts,  for  the  area  (jf  its  section,  which  product 
multiply  by  its  velocity  per  second  in  feet  and  parts,  and 
the  product  is  the  cubic  feet  used  per  second,  which 
multiplied  by  62,51b.  tlie  weight  of  1  cubic  foot,  pro- 


92  HYDRAULICS.  [Chap.  12 

duces  the  weight  of  water  per  second,  that  falls  on  the 
wheel,  which  multiplied  by  its  whole  perpendicular  de- 
scent, gives  a  true  measure  of  its  power. 

PROBLEM  L 

Given,  a  mill  seat  with  16  feet  fall,  width  of  the  canal 
5,333  feet,  depth  3  feet,  velocity  of  the  water  passing 
along  it  2,03  feet  per  second,  required  the  power  per 
second. 

Then,  5,333x3=15,999  feet,  the  area  of  the  section 
of  the  stream,  multiplied  by  20,3  feet,  tlie  velocity,  is 
equal  82,^  cubic  feet,  the  quantity  per  second,  multiplied 
by  65,5  is  equal  :^025lb.  the  weight  of  the  water  per  se- 
cond, multiplied  by  16,  the  perpendicular  descent,  is 
equal  32400,  for  the  power  of  the  seat  per  second. 

PROBLEM  IL 

Given,  the  perpendicular  descent  18,3,  width  of  the 
gate  2,66  feet,  height  ,145  of  a  foot,  velocity  of  the  wa- 
ter per  second,  issuing  on  the  wheel  15,76  feet,  required 
the  power. 

Then,  266x,145=,3857  the  area  of  the  gate,  x  15,76 
the  vel()city=6,178  cubic  feet,  expended  per  second 
x62,5=375,81b.  per  second  xl8,3  feet  perpendicular 
desceiit=6877  for  the  measure  of  the  power  per  second, 
which  ground  3,75lb.  per  minute,  equal  3,75  bushels  in 
an  hour,  \vith  a  five  feet  pair  of  burr  stones. 


ART.    54. 

INVESTfGxVTION  OF  THE   PRINCIPLES  OF  OVERSHOT  MILLS, 

Some  have  asserted,  and  many  believed,  that'  water  is 
applied  to  great  disadvantage  on  the  principle  of  an  over- 
shot mill ;  because,  say  they,  there  are  never  more  than 
two  buckets,  at  once,  that  can  be  said  to  act  fairly  on 
the  end  of  the  lever,  as  the  arms  of  the  wheel  are  called 
in  these  arguments.  But  we  must  consider  well  the  laws 
of  bodies  descending  inclined  planes,  and  curved  sur- 
faces.   See  art.  10,  11.     This  matter  will  be  cleared  up, 


Chap.  12.]  HYDRAULICS.  93 

if  we  consider  the  circumference  of  the  wheel  to  be  the 
curved  surface  :  for  the  fact  is,  tliat  the  water  acts  to 
the  best  advantage,  and  produces  effects  equal  to  what 
it  would,  in  case  the  whole  of  it  acted  upon  the  very  end 
of  the  lever,  in  the  whole  of  its  perpendicular  descent.* 

DEMONSTRATION. 

Let  A  B  C,  Plate  III.  fig.  20,  represent  a  water-wheel, 
and  F  H  a  trunk,  bringing  water  to  it  from  a  16  feet  head. 
Now  suppose  F  G  and  16  H  to  be  two  penstocks  under 
equal  heads,  down  which  the  water  descends,  to  act  on 
the  wheel  at  C,  on  the  principle  of  an  undershot,  on  op- 
posite sides  of  the  float  C,  with  equal  apertures.     Now 
it  is  evident  from  the  principles  of  hydrostatics,  shewTi  by 
the  paradox,  (art.  48,  and  the  first  law  of  spouting  fluids 
art.  45,)  that  the  impulse  and  pressure  will  be  equal 
from  each  penstock  respectively.     Although  the  one  be 
an  inclined  plane,  and  the  other  a  perpendicular,  their 
forces  are  equal,  because  their  perpendicular  heights  are ; 
(art.  4?8)  therefore  the  wheel  will  remain  at  rest,  because 
each  side  of  the  float  is  pressed  on  by  a  column  of  water 
of  equal  size  and  height,  as  represented  by  the  lines  on 
each  side  of  the  float.     Then  suppose  we  shut  the  pen- 
stock F  G,  and  let  the  water  down  the  circular  one  r  x, 
which  is  close  to  the  point  of  the  buckets  ;  this  makes  it 
obvious,  from  the  same  principles,  that  the  wheel  will  be 
held  in  equilibrio,  if  the  columns  of  each  side  be  equal. 
For,  although  the  column  in  the  circular  penstock,    is 
longer  than  the  perpendicular  one,  yet,  because  part  of 
its  weight  presses  on  the  lower  side  of  the  penstock,  its 
pressure  on  the  float  is  only  equal  to  the  perpendicular. 

Then,  again,  suppose  the  column  of  water  in  the  cir- 
cular penstock,  to  be  instantly  thrown  into  the  buckets, 
it  is  evident,  that  the  wheel  will  still  be  held  in  equilibrio, 
and  each  bucket  will  then  bear  a  proportional  part  of 
the  column,  that  the  bucket  C  bore  before  ;  and  that 
part  of  the  weight  of  the  circular  column,  which  rested 
on  the  under  side  of  the  circular  penstock,  is  now  on  the 

*  This  error  has  been  the  cause  of  many  expensive  errors  in  the  appli- 
cation oF  water. 


94  HYDRAULICS.  [Chap.  12. 

gudgeons  of  the  wheel.  This  shews  that  the  effect  of  a 
stream,  applied  on  an  overshot  wheel,  is  equal  to  the 
effect  of  the  same  stream,  applied  on  the  end  of  the  lever, 
in  its  whole  perpendicular  descent,  as  in  fig.  21,  where 
the  water  is  shot  into  the  buckets  fastened  to  a  strap  or 
chain,  revolving  over  two  wheels;  and  here  the  whijle 
force  of  the  gravity  of  the  column  acts  on  the  very  end 
of  the  lever,  in  the  whole  of  the  descent.  Yet,  because 
the  length  of  the  column  in  action,  in  this  case,  is  only 
16  feet ;  whereas  on  a  16  feet  wheel  the  length  of  the 
column  in  action  is  25,15,  therefore  the  powers  are 
equal. 

Again,  if  we  divide  the  half  circle  into  3  inches  Ab, 
be,  eC,  the  centre  of  gravity  of  the  upper  and  lower 
arches,  will  fall  near  the  point  a,  3,9  feet  from  the  centre 
of  motion,  and  the  centre  of  gravity  of  the  middle  arch, 
near  the  point  o,  7,6  feet  from  the  centre  of  motion.  Now 
each  of  these  arches  is  8,38  feet,  and  8,38x2x3,9=6.^,36, 
and  8,38x7,6  feet=63,07,  which  two  products  added= 
128,13,  for  the  momentum  of  the  circular  column,  by 
the  laws  of  the  lever,  and  for  the  perpendicular  column 
16x8  the  radius  of  the  wheel=128,  for  the  momentum  ; 
by  which  it  appears,  that  if  we  could  determine  the  exact 
points  on  which  the  arches  act,  the  momentums  would 
be  equal,  all  which  shews,  that  the  power  of  water  on 
overshot  wheels,  is  equal  to  the  whole  power  it  can  any 
way  produce,  through  the  M^hole  of  its  perpendicular 
descent,  except  what  may  be  lost  to  obtain  velocity,  (art. 
41)  overcome  friction,  or  by  part  of  the  water  spilling, 
before  it  gets  to  the  bottom  of  the  wheel.     Q.  E.  D. 

I  may  add,  that  I  have  made  the  following  experi- 
ment, viz.  I  fixed  a  truly  circular  wheel  on  nice  pivots, 
to  evade  friction,  and  took  a  cylindric  rod  of  thick  wire, 
cutting  one  piece  exactly  the  length  of  half  the  circum- 
ference of  the  wheel,  and  fastening  it  to  one  side,  close 
to  the  rim  of  the  wheel  its  whole  length,  as  at  G  x  r  a.  I 
then  took  another  piece  of  the  same  wire,  of  a  length 
equal  to  the  diameter  of  the  wheel,  and  hung  it  on  the 
opposite  side,  on  the  end  of  the  lever  or  arm,  as  at  B., 
and  the  wheel  was  in  equilibrio.     Q.  E.  D. 


Chap.  12.J  HYDRAULICS.  95 

ART.    55. 

OF  THE  FRICTION  OF  THE  APERTURES  OF  SPOUTING  FLUIDS. 

The  doctrine  of  this  species  of  friction  appears  to  be 
as  follows; 

1.  The  ratio  of  the  friction  of  round  apertures,  are  as 
their  diameters,  nearly,  while  their  quantities  expended, 
are  as  the  squares  of  their  diameters. 

2.  The  friction  of  an  aperture,  of  any  regular  or  irre- 
gular figure,  is  as  the  length  of  the  sum  of  the  circum- 
scribing lines,  nearly ;  the  quantities  being  as  the  areas 
of  the  aperture.*     Therefore, 

3.  The  less  the  head  )r  pressure,  and  the  larger  the 
apertnre,  the  less  the  ratio  of  the  friction;  therefore, 

4.  This  friction  need  not  be  much  regarded,  in  the 
large  openings  or  apertures  of  undershot  mills,  where 
the  gates  are  from  2  to  15  inches  on  their  shortest  sides ; 
but  it  very  sensibly  affects  the  small  apertures  of  high 
overshot  or  under  hot  mills,  with  great  heads,  where 
their  shortest  sides  are  from  five-tenths  of  an  inch  to  two 
inches.f 


ART.    .56. 
OF  THE  PRESSURE  OF  THE    \IR  ON  FLUIDS. 

The  second  cause  of  the  motion  or  rise  of  fluids,  is 
the  pressure  of  the  air  on  the  surface  of  them,  in  the 

•  This  will  .-^pp -ar,  if  we  consWler  ami  suppose,  that  the  friction  does 
sensibly  retard  the  velocity  of  ih>-  fluid  to  a  certain  distance.  Say  halt  an 
inch  from  the  side  or  edge  of  the  aperture,  towards  its  centre  ;  and  we 
may  reasonably  coiicliiiie,  that  this  distance  will  be  nearly  the  same  in  a  2 
and  12  inch  apertme;  so  that  in  tlie  2  inch  aperture,  a  ring  on  the  out- 
side, half  an  inch  wide,  is  sensibly  retarded,  which  is  about  3-4  of  ;he 
whole  ;  while,  in  t|it-  12  inch  pe  lure,  there  is  a  ring  on  the  outside  half 
an  inch  wide,  retarded  about  1  6  of  its  ^vhoie  area. 

t  This  seems  to  tf  proved  by  S'lieaion,  in  h  s  experiments;  (see  table, 
art.  67  )  where,  when  the  heail  w  .s  33  nchts,  the  sluice  small,  dra^vnonly 
to  the  1st  hole,  the  velocity  was  only  such  as  is  assigned  by  iheory,  to  a 
head  of  15,85  inches,  which  hf  call.-,  virtual  head-  But  when  the  sluice  was 
larjjer,  drawn  to  the  6  h  hole,  and  head  6  inches,  the  virtual  head  was  5,33 
inches.  But  seeing  there  is  no  theorem  yet  discovered  by  which  we  can 
truly  de'ermine  the  quantity  or  efiec  of  their  friction,  according  to  the 
size  of  the  aperture,  and  height  of  the  head  ;  therefoie,  we  cannot,  by  the 
established  laws  of  hydrostatirs,  df 'ermine  exa  tly  'he  velocity  or  quan- 
tity expended  ihrotigh  any  bmall  apevmre;  which  renders  the  theory  but 
little  belter  than  conjecture  in  these  cases. 


96  HYDRAULICS.  [Chap.  12. 

fountain  or  reservoir;  and  this  pressure  is  equal  to  a 
head  of  water  of  33  1-3  feet  perpendicular  height,  under 
which  pressure  or  height  of  head,  the  velocity  of  spout- 
ing water  is  46,73  feet  per  second. 

Therefore,  if  we  could  by  any  nleans  take  off  the 
pressure  of  tlie  atmosphere,  from  any  one  part  of  the 
surface  of  a  fluid,  that  part  would  spout  up  with  a  velo- 
city of  46,73  feet  per  second,  and  rise  to  the  height  of 
33  1-3  feet  nearly.^ 

On  this  principle  act  all  syphons  or  cranes,  and  all 
pumps  for  raising  water  by  suction,  as  it  is  called. — Let 
fig.  23,  pi.  in.  represent  a  cask  of  water,  with  a  syphon 
therein,  to  extend  33  1-3  feet  above  the  surface  of  the 
water  in  the  cask.  Now  if  the  bung  be  made  perfectly 
air-tight,  round  the  syphon,  so  that  no  air  can  get  into 
the  cask,  and  the  cask  be  full,  then,  if  all  the  air  be 
drawn  out  of  the  syphon,  at  the  bended  part  A,  the  fluid 
will  not  rise  in  the  syphon,  because  the  air  cannot  get 
to  it  to  press  it  up  ;  but  take  out  the  plug  P,  and  let  the 
air  into  the  cask,  to  press  on  the  surface  of  the  water, 
and  it  will  spout  up  the  short  leg  of  the  syphon  B  A, 
with  the  same  force  and  velocity,  as  if  it  had  been  press- 
ed with  a  head  of  water  33  1-3  feet  high,  and  will  run 
into  the  long  leg  and  will  fill  it.  Then  if  we  turn  the 
cock  c,  and  let  the  water  run  out,  its  weight  in  the  long 
leg  will  overbalance  the  weight  in  the  short  one,  drawing 
the  water  out  of  the  cask  until  the  water  sink  so  low, 
that  the  leg  B  A  will  be  33  1-3  feet  high,  above  the  sur- 
face of  the  water  in  the  cask  ;  then  it  will  stop,  because 
the  weight  of  water  in  the  leg,  in  which  it  rises,  will  be 
equal  to  the  weight  of  a  column  of  the  air  of  equal  size, 
and  of  the  whole  height  of  the  atmosphere.  The  waiex 
will  not  run  out  of  the  leg  A  c,  but  will  stand  full  33  1-3 

•  This  seems  to  be  the  principle  of  whirlwind*  at  sea,  called  water 
spouts;  the  wind  meeting-  from  different  points,  forms  a  qiMck  circiilai* 
motion;  and  by  the  centrifugal  force  forms  a  partial  vacuum  in  the  cen- 
tre, which  gives  liberty  to  the  water  to  rise  a  little,  which  is  by  the  rapid- 
ity of  the  motion  of  the  air,  rent  into  very  small  particles  :  which  so  in- 
creases the  surface,  that  the  air  takes  sufficient  hold  of  it  to  carry  it  up. 
And  as  the  wind  meeting  has  no  way  to  vent  itself  but  in  a  perpendicular 
direction,  therefore,  a  brisk  current  is  formed  upwards,  carrying  th(  wa- 
ter with  it,  at  sea;  but  on  the  land,  it  raises  leaves  of  trees  and  other 
light  bodies.     See  Franklin's  Letters. 


Chap.  12.]  HYDRAULICS.  97 

feet  above  its  mouth,  because  the  air  will  press  up  the 
mouth  c,  with  a  force  that  will  balance  30  1-3  feet  of 
water  in  the  leg  c  A.  This  will  be  the  case,  let  the  up- 
per part  of  the  leg  be  any  size  whatever — and  there  will 
be  a  small  vacuum  in  the  top  of  the  long  leg. 


ART.    57. 
OF  PUMPS. 

Let  fig.  24,  pi.  in.  represent  a  pump  of  the  common 
kind  used  for  drawing  water  out  of  wells.  The  move- 
able valve  or  bucket  A,  is  cased  with  leather,  which 
springs  outwards,  and  fits  the  tube  so  nicely,  that  neither 
air  nor  water  can  pass  freely  by  it.  When  the  lever  L 
is  worked,  the  valve  A  opens  as  it  descends,  letting  the 
air  or  water  pass  through  it.  As  it  ascends  again  the 
valve  shuts ;  the  water  which  is  above  the  bucket  A  is 
raised,  and  there  would  be  a  vacuum  between  the 
valves,  but  the  weight  of  the  air  presses  on  the  surface 
of  the  water  in  the  well,  at  W,  forcing  it  up  through  the 
valve  B,  to  fill  the  space  between  the  buckets :  and  as 
the  valve  A  descends,  B  shuts,  and  prevents  the  water 
from  descending  again  :  But  if  the  upper  valve  A  be 
set  more  than  33  1-3  feet  above  the  surface  of  the  water 
in  the  well,  the  pump  cannot  be  made  to  draw,  because 
the  pressure  of  the  atmosphere  will  not  cause  the  water 
to  rise  more  than  33  1-3  feet. 


9S 


HYDRAULICS. 


[Chap.  12 


A  TABLE  FOR  PUMP.MAKERS. 


Height    of    the 

Diameter  of 

Water  discharged 

pump  in  feet 

the  bore. 

in   a    minute   m 

above  the  snr- 

o 

wine  measure. 

face    of     the 

3               a  (-5 

well. 

1  pans 
1  inch. 

i 
ches. 

81                        6 

10 

6            93 

15 

5            66 

54                        4 

20 

4            90 

40                       7 

25 

4            38 

32                       6 

30 

4            GO 

27                       2 

35 

3            70 

23                       3 

40 

3            46 

20                       3 

45 

3             27 

18                       1 

50 

3             10 

16                       3 

55 

2             95 

14                      7 

60 

?             84 

13                      5 

65 

2            72 

12                       4 

70 

2            62 

11                       5 

75 

2            53 

10               r 

80 

2            45 

10                      2 

85 

2            38 

9                       5 

90 

2            31 

9                       1 

95 

2            25 

8                       5 

"  100 

2             19 

8                      1 

"  All  pnmps  should  be  so  constructed  as  to  work  with  equal  ease,  in 
raising  the  water  to  any  {jiven  heijihi  above  the  surface  of  the  well  and 
this  may  be  done  by  observing  a  due  proportion  between  the  diameter  of 
that  part  of  the  piim'p'bore  in  which  the  piston  or  bucket  works,  and  the 
height  to  which  the  water  must  be  raised. 

"  For  this  purpose  I  have  calculated  the  above  table,  in  which  the  handle 
of  the  pump  is  ssipposed  to  be  a  lever,  increasing  the  power  five  limes  : 
that  is,  the  distance  or  length  of  that  part  of  the  handle  that  lies  between 
the  pin  on  which  it  moves,  and  the  top  of  the  pumprod  to  which  it  is  fix- 
ed, to  be  only  one  fifth  part  of  the  length  of  the  handle,  from  the  said  pin 
to  the  part  where  the  man  (who  works  the  pump)  applies  his  force  or 
power. 

"  In  the  first  column  of  the  table,  find  the  height  at  which  the  pump 
must  discharge  the  water  above  the  surface  of  the  well ;  then  in  the  second 
column,  you  have  the  diameter  of  that  part  of  the  bore  in  which  the  pis- 
ton or  bucket  works,  in  inches  and  hundredth  parts  of  an  inch;  in  the 
third  column  is  the  quantity  of  water,  (in  mine  weasure)  that  a  man  of 
common  strength  can  raise  in  a  minute — And  by  constructing  according 
to  this  method,  pumps  of  all  heights  may  be  vi'roni^ht  by  a  man  of  ordinary 
streiiKlh  so  as  to  be  able  to  hold  out  for  an  hour." 

JAMES  FERGUSON. 


Chap.  I2.j  HYDRAULICS.  99 


ART.  58. 

OF  CONVEYING  WATER  ^NDER  VALLEYS  AND  OVER  HILLS, 

Water,  by  its  pressure,  and  the  pressure  of  the  atmos- 
phere, may  be  conveyed  under  valleys  and  over  hills,  to 
supply  a  family,  a  mill,  or  a  town.  See  fig.  20,  pi.  III. 
F  H  is  a  canal  for  conveying  water  to  a  mill-wheel. 
Now  let  us  suppose  F  G  16  H  to  be  a  tight  tube  or 
trunk — the  water  being  let  in  at  F,  it  will  descend  from 
F  to  G,  and  its  pressure  at  F  will  cause  it  to  rise  to  H, 
passing  along  if  permitted,  and  may  be  conveyed  over  a 
hill  by  a  tube,  acting  on  the  principle  of  the  syphon, 
(art.  56.)  But  w'here  some  have  had  occasion  thus  to 
convey  water  under  any  obstacle  for  the  convenience  of 
a  mill,  which  often  occurs  in  practice,  they  have  gone 
into  the  following  expensive  error  :  They  make  the  tube 
at  G  16  smaller  than  if  it  had  been  on  a  level,  because, 
say  they,  a  greater  quantity  will  pass  though  a  tube, 
pressed  by  the  head  G  F,  than  on  a  level.  But  they 
should  consider  that  the  head  G  F  is  balanced  by  the 
head  H  16,  and  the  velocity  through  the  tube  G  16  will 
only  be  such  that  a  head  equal  to  the  difference  between 
tlie  perpendicular  height  of  G  F  and  H  16  would  give  it; 
(see  art.  41,  fig.  19,)  therefore  it  should  be  as  large  at  G 
16  as  if  on  a  level. 


ART.    59. 

OF  THE  DIFFERENCE  OF  THE  FORCE  OF  INDEFINITE  AND  DE- 
FINITE QUANTITIES  OF  WATER  STRIKING  A  Vv^HEEL. 

DEFINITIONS. 

1.  By  an  indefinite  quantity  of  water  we  here  mean  a 
river  or  large  quantity,  much  larger  than  the  float  of  the 
Avheel,  so  that,  when  it  strikes  the  float,  it  has  liberty  to 
move  or  escape  from  it  in  every  lateral  direction. 


100  HYDRAULICS.  [Chap.  12. 

2.  By  a  definite  quantity  of  water  we  mean  a  quantity 
passing  throus^h  a  given  aperture  along  a  shute  to  strike 
a  wheel ;  but  as  it  strikes  the  float,  it  has  liberty  to  escape 
in  every  lateral  direction. 

3.  By  a  perfectly  definite  quantity,  we  mean  a  quan- 
tity passing  along  a  close  tube  so  confined,  that  when  it 
strikes  the  float,  it  has  not  liberty  to  escape  in  any  lateral 
direction. 

First,  When  a  float  of  a  wheel  is  struck  by  an  indefi- 
nite quantity,  the  float  is  struck  by  a  column  of  water, 
the  section  of  which  is  equal  to  the  area  of  the  float ;  and 
as  this  column  is  confined  on  every  side  by  the  sur- 
rounding water,  which  has'tqual  motion,  it  cannot  escape 
freely  sideways ;  therefore  more  of  its  force  is  commu- 
nicated to  the  float  than  would  be,  in  case  it  had  free  li- 
berty to  escape  sideways  in  every  direction. 

Secondly,  The  float  being  struck  by  a  definite  quan- 
tity, with  liberty  to  escape  freely  in  every  side  direction, 
it  acts  as  the  most  perfect  non- elastic  body ;  therefore 
(by  art.  8)  it  communicates  only  a  part  of  its  force,  the 
other  part  being  spent  in  the  lateral  direction.  Hence  it 
appears,  that  in  the  application  of  water  to  actiDy  im- 
pulse, we  should  draw  the  gate  as  near  as  possible  to  the 
float- board,  and  confine  it  as  much  as  possible  from 
escaping  sideways  as  it  strikes  the  float ;  but,  taking 
care  at  the  same  time,  that  we  do  not  bring  the  principle 
of  the  Hydrostatic  Paradox  into  action,  (art.  48.) 

What  proportion  of  the  force  of  the  water  is  spent  in 
a  lateral  direction  is  not  yet  determined,  but  see  Art.  8. 

4.  A  perfectly  definite  quantity  striking  a  plane,  com- 
municates its  whole  force  ;  because  no  part  can  escape 
sideways,  and  is  equal  in  power  to  an  elastic  body,  or 
the  weight  of  the  water  on  an  overshot  wheel,  in  its 
whole  perpendicular  descent.  But  this  application  of 
water  to  wheels  has  been  hitherto  impracticable ;  for 
whenever  we  attempt  to  confine  the  water  totally  from 
escaping  sideu  ays,  we  bring  the  paradoxical  principle  into 
action,  which  defeats  the  scheme.* 

•  But  this  difficulty  is  no^v  overcome  by  the  valve  wheel.  See  annotation, 
art.  7\i. 


Chap.  12.]  HYDRAULICS.  101 

To  make  this  plain,  let  fig.  25,  pi.  III.  be  a  water- 
wheel  ;  and  first,  let  us  suppose  the  water  to  be  brought 
to  it  by  the  penstock  4.16,  to  act  by  impulse  on  the  float 
board,  having  free  liberty  to  escape  every  uay  as  it  strikes; 
then  by  art.  8,  it  will  communicate  but  half  its  force. 
But  if  it  be  confined  both  at  sides  and  bottom  and  can 
escape  only  upwards,  to  which  tlie  gravity  will  make 
some  opposition,  it  will  communicate  perhaps  more  than 
half  its  force,  and  will  not  re-act  back  against  the  float 
c.  But  if  we  put  soaling  to  the  wheel'  to  prevent  the 
water  from  escaping  upwards,  then  the  space  between 
the  floats  will  be  filled,  as  soon  as  the  wheel  begins  to 
be  retarded,  and  the  paradoxical  principle,  art.  48,  is 
brought  fully  into  action  viz.  the  pressure  of  water  is 
every  way  equal,  and  presses  backwards  against  the  bot- 
tom of  the  float  c,  with  a  force  equal  to  its  pressure  on 
the  top  of  the  float  b,  and  the  wheel  will  immediately  stop 
and  be  held  in  equilibrio,  and  will  not  start  again  although 
all  resistance  be  removed.  This  we  may  call  the  para- 
doxical mill.  There  are  many  mills,  where  this  principle 
is,  in  part,  brought  into  action,  which  very  much  lessens 
their  power. 


ART.    60. 
OF  THE  MOTION  OF  BREAST  AND  PITCHBACK  WHEELS. 

Many  have  been  of  opinion,  that  when  water  is  put  to 
act  on  the  wheel  as  at  a  (called  a  low  breast)  with  12 
feet  head,  that  then  the  4  feet  fall  below  the  point  of 
impact  a,  is  totally  lost,  because,  say  they,  the  impulse 
of  the  12  feet  head,  will  require  the  wheel  to  move  with 
such  velocity  to  suit  the  motion  of  the  water  as  to  move 
before  the  action  of  gravity,  therefore  the  water  cannot 
act  after  the  stioke.  But  if  they  will  consider  well  the 
principles  of  gravity  acting  on  falling  bodies  (art.  9), 
they  will  find,  that,  if  the  velocity  of  a  falling  body  be 


1£)2  HYDRAULICS.  [Ghap.  12. 

ever  so  great,  the  action  of  gravity  is  still  the  same  to 
cause  it  to  move  faster,  so  that,  although  an  overshot 
wheel  may  move  before  the  power  of  the  gravity,  of  the 
water  thereon,  yet  no  impulse  downwards  can  give  a 
wheel  such  velocity,  as  that  the  gravity  of  the  water  act- 
ing thereon  can  be  lessened  thereby.* 

Hence  it  appears,  that  when  a  greater  head  is  used, 
than  what  is  necessary  to  shoot  the  water  fairly  into  the 
wheel,  the  impulse  should  be  directed  downward  a  little 
as  at  D,  (which  is  called  pitch-back,)  and  have  a  cir- 
cular sheeting  to  prevent  the  water  from  leaving  the 
wheel,  because  if  it  be  shot  horizontally  on  the  top  of  a 
wheel,  the  impulse  in  that  case  will  not  give  the  water 
any  greater  velocity  downwards ;  then,  in  this  case,  the 
fall  would  be  lost,  if  the  head  was  very  great,  and  the 
wheel  moved  to  suit  the  velocity  of  the  impulse,  the 
water  would  be  thrown  out  of  the  buckets  by  the  centri- 
fugal force  ;  and  if  we  attempt  to  retard  the  wheel,  so  as 
to  retain  the  water,  the  mill  will  be  so  ticklish  and  unstea- 
dy, that  it  will  be  almost  impossible  to  attend  it. 

Hence  may  appear  the  reason  why  breast-wheels  ge- 
nerally run  quicker  than  overshots,  although  the  fall  after 
the  water  strikes  be  not  so  great. 

1.  There  is  generally  more  head  allou^ed  to  breast- 
mills  than  overshots,  and  the  wheel  will  incline  to  move 
with  nearly  2-3  the  velocity  of  the  water,  spouting  from 
under  the  head,  (art.  41.) 

2.  If  the  water  was  permitted  to  fall  freely  after  it 
issues  from  the  gate,  it  would  be  accelerated  by  the  fall, 
so  that  its  velocity  at  the  lowest  point  would  be  equal 
to  its  velocity,  had  it  spouted  from  under  a  head  equal 
to  its  whole  perpendicular  descent.  This  accelerated 
velocity  of  the  water,  tends  to  accelerate  the  wheel; 
hence,  to  find  the  velocity  of  a  breast- wheel,  where  the 
water  is  struck  on  in  a  tangent  direction  as  in  fig.  31, 
32,  I  deduce  the  following 

*  if  gravity  could  be  either  decreased  by  velocity  downwards,  or  increased 
by  velocity  upwards,  then  a  vertical  wheel  without  friction,  either  of  gud- 
geons or  air,  would  require  a  great  force  to  continue  its  motion ;  because, 
its  velocity  would  decrease  the  gravity  of  its  descending  side,  and  increase 
it  on  its  ascending  side,  which  would  immediately  stop  it  :  whereas  it  is 
known,  that  it  requires  no  power  to  continue  its  motion,  but  what  is  neces- 
sary to  overcome  the  friction  of  the  gudgeons,  &c. 


Chap.  12.]  HYDRAULICS.  103 


THEOREM. 

1.  Find  the  difference  of  the  velocity  of  the  water 
under  the  head  allowed  to  the  wheel,  above  the  point  of 
impact,  and  the  velocity  of  a  falling  body,  having  fell 
the  whole  perpendicular  descent  of  the  water.  Call 
this  difference  the  acceleration  by  the  fall :  Then  say, 
As  the  velocity  of  a  falling  body  acquired  in  falling 
tlirough  the  diameter  of  any  overshot  wheel,  is  to  the 
proper  velocity  of  that  wheel  by  the  scale,  (art.  43)  so 
is  the  acceleration  by  the  fall,  to  the  acceleration  of  the 
wheel  by  the  fall,  after  the  water  strikes  the  wheel. 

2.  Find  the  velocity  of  the  water  issuing  on  the 
wheel ;  take  ,577  of  said  velocity ,  to  which  add  the 
accelerated  velocity,  and  that  sum  will  be  the  velocity 
of  the  breast- wheel. 

This  rule  will  hold  nearly  true,  when  the  head  is  con- 
siderably greater  than  is  assigned  by  the  scale  (art.  43) ; 
but  as  the  head  approaches  that  assigned  by  the  scale, 
tliis  rule  will  give  the  motion  too  quick. 

EXAMPLE. 

Given,  a  high  breast-wheel,  fig.  25,  where  the  water 
is  shot  on  at  d,  the  point  of  impact — 6  feet  head,  and 
10  feet  fall — required  the  motion  of  the  circumference 
of  the  wheel,  working  to  the  best  advantage,  or  maxi- 
mum effect. 
Then,  the  velocity  of  the  water,  issuing  ?  i  q  q^  p 

on  the  wheel,  6  feet  head,  5  ^^'"^^  *^^^- 

The  velocitv  of  a  falling  body,  having  16  2.  qo  a     ri 

feet  fall,  the  whole  descent,  5  ^^'^    ^°' 

Difference,  -         -         13,06  do. 

Then,  as  the  velocity  under  a  16  feet  fall  (32,4  feet) 
is  to  the  velocity  of  an  overshot  wheel=8,76  feet,  so  is 
13,06  feet,  to  the  16  feet  diameter  velocity  accelerated, 
which  is  equal  3,5  feet,  to  which  add,  577  of  19,34  feet 
(being  11,15  feet);  this  amounts  to  14,65  feet  per  second, 
^he  velocity  of  the  breast-wheel. 


104  HYDRAULICS.  [Chap.  U, 


ART.    61. 


RULE  FOR  CALCULATING  THE  POWER  OF  ANY  MILL-SEAT. 

The  only  loss  of  power  sustained  by  usinj;  too  much 
head,  in  the  application  of-  water  to  turn  a  mill-wheel, 
is  from  the  head  producing  only  half  its  po\ver.  There- 
fore, in  calculating  the  power  of  16  cubic  feet  per  se- 
cond, on  the  different  applications  of  fig.  25,  pi.  III.  we 
must  add  half  the  head  to  the  whole  fall,  and  count  that 
sum  the  virtual  perpendicular  descent.  Then  by  theo- 
rem IV.  (art.  53)  multiply  the  weight  of  the  water  per 
second  by  its  perpendicular  descent,  and  you  have  the 
true  measures  of  its  power. 

But  to  reduce  the  rule  to  a  greater  simplicity,  let  us 
call  each  cubic  foot  1,  and  the  rule  will  be  simply  this — 
Multiply  the  cubic  feet  expended  per  second,  by  its  vir- 
tual perpendicular  descent  in  feet,  and  the  product  will 
be  a  true  measure  of  the  power  per  second.  This  mea- 
sure must  have  a  name,  which  I  call  Cuboch ;  that  is, 
one  cubic  foot  of  water,  multiplied  by  one  foot  descent, 
is  one  cuboch,  or  the  unit  of  power. 

EXAMPLES. 

1.  Given,  16  cubic  feet  of  water  per  second,  to  be 
applied  by  percussion  alone,  under  16  feet  head,  re- 
quired the  power  per  second. 

Then,  half  16=8x16=128  cubochs,  for  the  measure 
of  the  power  per  second. 

2.  Given,  16  cubic  feet  per  second,  to  be  apj^lied  to 
a  half  breast  of  4  feet  fall  and  12  feet  head,  required  the 
power. 

Then,  half  13=6+4=10x16=160  cubochs,  for  the 
power. 

3.  Given,  16  cubic  feet  per  second,  to  be  applied  to  a 
pitch-back  or  high  breast — fall  10,  head  6  feet,  required 
the  power. 


Chap.  12.]  HYDRAULICS.  1(^5 

Then,  half  6=3+13=10xl6=S08  cubochs,  for  the 
power  per  second. 

4.  Given,  16  cubic  feet  of  water  per  second,  to  be 
applied  as  an  ov^ershot^ — head  4,  fall  IS  feet,  required  the 
power. 

Then,  half  4=3+ 1 2=1 4x  16=231  cubochs,  for  the 
power. 

The  powers  of  equal  quantities  of  water  16  cubic  feet 
per  second,  and  equal  total  perpendicular  descents  by  the 
different  applications,  stand  thus  : 

C  16  feet  head,* 
The  undershot,     <  0  fall, 

(128  cubochs  of  power. 
C  12  feet  head, 
The  half  breast,     <  4  feet  fall, 

(  160  cubochs  of  power. 
C  6  feet  head, 
The  high  breast,   <  10  feet  fall, 

(  208  cubochs  of  power. 
C  4  feet  head, 
The  overshot,        <  12  feet  fall, 

(  224  cubochs  of  power- 
C  2,5  feet  head. 
Ditto,  <  31,5  feet  fall, 

{  263  cubochs  of  power. 
The  last  being  the  head  necessary  to  shoot  the  watei; 
feirly  into  the  buckets,  may  be  said  to  be  the  best  appli- 
cation.    See  art.  43. 

•  Water  by  percussion  spends  its  force  on  the  wheel  in  the  following^ 
time,  which  is  in  proportion  to  the  distance  of  the  float-board,  and  diffcF- 
cnce  of  the  velocity  of  the  water  and  wheel. 

If  the  water  runs  wit!)  double  the  velocity  of  the  wheel,  it  will  spend 
all  its  force  on  the  floats,  while  the  water  runs  the  distance  of  two  float- 
boards,  and  while  the  wheel  runs  the  distance  of  one  ;  therefore  the  water 
need  not  be  kept  to  act  on  the  wheel  from  the  point  of  impact  further  than 
the  distance  of  about  two  float-boards. 

But  if  the  wheel  runs  with  two-thirds  of  the  velocity  of  the  water,  then, 
while  the  wheel  runs  the  distance  of  two  floats,  and  while  the  water  would 
have  ran  the  distance  of  three  floats,  it  spends  all  its  force  ;  therefore  the 
water  need  be  kept  to  act  on  the  wheel  only  the  distance  of  three  floatf 
past  the  point  of  impact. 

If  it  be  continued  in  much  longer  it  will  fsdl  back,  and  re-act  against  the 
following'  bucket  and  retard  the  wheel. 

Q 


106 


HYDRAULICS. 


[Chap.  12. 


On  these  simple  rules,  and  the  rule  laid  down  in  art. 
43,  for  proportioning  the  head  and  fall,  I  have  calculated 
the  following  table  or  scale  of  the  different  quantities  of 
water  expended  per  second,  with  different  perpendicular 
descents,  to  produce  a  certain  power,  in  order  to  present 
at  one  view  to  the  reader  the  ratio  of  increase  or  decrease 
of  quantity,  as  the  perpendicular  descent  increases  or 
decreases. 


A  TABLE 

Shewin.^  the  quantity  of  water  required  with  different  falls,  to  produce  by- 
its  gravity,  112  ciitiochs  of  power,  wliich  will  drive  a  five  feet  stone  about 
^7  revolutions  in  a  minute,   grinding  wheat  about  5  bushels  in  an  hour 


r^ 

c 

H 

0 

-•  S5  s  s" 

c 

-..»«- 

c 

cr 
n 

01      Cl^    rj-     < 

0; 
0 

s  n 

q-  ft  ft  - 

"■  0 

c   ^ 

5:  =35    0. 

ft  5: 

esce 
half 
the 

e  wl 

3   5 

9-^ 

0  s 

3    ft 
CL  -> 

—      -*-   r»     3 

9?  -■ 

""       -•-    r-      — 

•       -5 

?.£^; 

►5 

■     p:   rr  -^ 

c 

p-   ^  "** 

^^ 

^  t  ^ 

•^ 

"♦:  ft    ^- 

•-; 

Q    »:    ~ 

m 

n   s"   ^ 

ft 

-:   O-ns 

Tit 

c 

1 

112 

16 

7, 

2 

56 

17 

6,58 

3 

2.7,3 

18 

6,y2 

4 

28 

19 

5,99 

5 

224 

20 

5,6 

6 

18,6 

21 

5,33 

7 

16, 

22 

5,1 

8 

14 

23 

4,87 

9 

12,4 

24 

4,66 

10 

11,2 

25 

4,48 

11 

10,2 

26 

4,3 

12 

9,33 

27 

4,15 

13 

8,6 

28 

4, 

14 

8, 

29 

3,86 

15 

7,46 

30 

•^,7i 

ART.    62. 
THEORY  AND  PRACTICE  COxMPARED. 

I  will  here  give  a  table  of  18  mills  in  actual  practice 
out  of  about  50  that  I  have  taken  an  account  of,  in  order 


6hap.  12.]  HYDRAULICS.  lOr 

to  compare  theory  with  practice,  and  in  order  to  ascer- 
tain the  power  required  on  each  superficial  foot  of  the 
acting  parts  of  the  stone  :  But  I  must  premise  the  fol- 
lowing 

THEOREMS. 

1.  To  find  the  circumference  by  the  diameter,  or  the 
diameter  by  the  circumference  of  a  circle  given ;  say. 

As  7  is  to  22,  so  is  the  diameter  of  the  stone  to  the  cir- 
cumference, i.  e.  Multiply  the  diameter  by  22,  and  di- 
vide the  product  by  7,  for  the  circumference  ;  or,  multi- 
ply the  circuniference  by  7,  and  divide  the  product  by 
22,  for  the  diameter. 

2.  To  find  the  area  of  a  circle  by  the  diameter  given  : 
As  1,  squared,  is  to  ,7854,  so  is  the  square  of  the  diaaie- 
ter  to  the  area  ;  i.  e.  Multiply  the  square  of  the  diameter 
by  ,7854,  and  deduct  1  foot  for  the  eye,  and  you  have 
the  area  of  the  stone. 

3.  To  find  the  quantity  of  surface  passed  by  a  mill- 
stone :  The  area,  squared,  multiplied  by  the  revolutions 
of  the  stone,  gives  the  number  of  superficial  feet,  passed 
in  a  given  time. 

OBSERVATIONS  ON  THE  FOLLOWING  TABLE  OF  EXPERIMENTS. 

I  have  asserted  in  art.  44,  that  the  head  above  the  gate 
of  a  wheel,  on  which  the  water  acts  by  its  gravity,  should 
be  such,  as  to  cause  the  water  to  issue  on  the  wheel, 
with  a  velocity  to  that  of  the  wheel  as  3  to  S,  to  compare 
this  with  the  following  table  of  experiments. 

1.  Exp.  Overshot.  Velocity  of  the  water  12,9  feet 
per  second,  velocity  of  the  wheel  8,S  feet  per  second, 
which  is  a  little  less  than  3-3  of  the  velocity  of  the  wa- 
ter. This  wheel  received  the  water  well.  It  is  at  Stan- 
ton, in  Delaware  state. 

2.  Overshot.  Velocity  of  the  water  11,17  feet  per 
second,  S-3  of  which  is  7,44  feet,  velocity  of  the  wheel 
8,5  feet  per  second.  This  received  the  water  pretty 
well.     It  is  at  the  above-mentioned  place. 

3.  Overshot.  Velocity  of  the  water  13,16  feet  per 
second,  velocity  of  the  wheel  10,3 ;  throws  out  great 


108  HYDRAULICS.  [Chap.  1^. 

part  of  the  water  by  the  back  of  the  buckets  ;  strikes  it 
and  makes  a  thumping  noise.  It  is  allowed  to  run  too 
fast ;  revolves  faster  than  my  theory  directs.  It  is  at 
Brandywine,  in  Delaware  state. 

4.  Overshot.  Velocity  of  the  water  14,4  feet  per  se- 
cond, velocity  of  the  wheel  9,3  feet,  a  little  less  than  2-3 
of  the  velocity  of  the  water.  It  receives  the  water  very 
well ;  has  a  little  more  head  than  assigned  by  theory, 
and  runs  a  little  faster ;  it  is  a  very  good  mill,  situate  at 
Brandywine,  in  the  state  of  Delaware. 

6.  Undershot.  Velocit}'  of  the  wheel,  loaded,  16,  and 
when  empty  24  revolutions  per  minute,  which  confirms 
the  theory  of  motion  for  undershot  wheels.  See  art.  42. 

7.  Overshot.  Velocity  of  the  water  15,79  feet,  velo- 
cit}'  of  the  wheel  7,8  feet ;  less  than  3-3  of  the  velocity 
of  the  water ;  motion  slower  and  head  more  than  as- 
signed by  theory.  The  miller  said  the  wheel  ran  too 
slow,  and  would  have  her  altered  ;  and  that  she  worked 
best  \\hen  the  head  was  considerably  sunk.  She  is  at 
Bush,  Hartford  county,  Maiyland. 

8.  Overshot.  Velocity'  of  the  water  14,96  feet  per 
second,  velocity  of  the  wheel  8,8  feet,  less  than  2-3,  very 
near  the  velocity  assigned  by  the  theory ;  but  the  head 
is  greater,  and  she  runs  best  when  the  head  is  sunk  a 
little  ;  is  counted  the  best  mill ;  and  is  at  the  same  place 
with  the  last  mentioned. 

9.  10,  11,  12.  Undershot,  open  wheels.  Velocity  of 
the  wheels  when  loaded  20  and  40,  and  when  empty  28 
and  56  revolutions  per  minute,  which  is  faster  than  my 
theory  for  the  motion  of  undershot  mills.  Ellicott's 
mills,  near  Baltimore,  in  Maryland,  serve  to  confirm  the 
theor}'. 

14.  Overshot.  Velocity  of  the  water  16,2  feet,  velo- 
city of  the  wheel  9,1  feet,  less  than  2-3  of  the  water, 
revolutions  of  the  stone  114  per  minute,  the  head  near 
the  same  as  by  theory,  the  ^•elocity  of  the  wheel  less, 
stone  more.  This  shev\s  her  to  be  too  high  geared. 
She  receives  the  water  well,  and  is  counted  a  very  good 
mill,  situate  at  Alexandria,  in  Virginia. 

15.  Undershot.  Velocity  of  the  water  24,8  per  se- 


Chap.  12.J  HYDRAULICS.  109 

cond,  velocity  of  the  wheel  16,67  feet,  more  than  S-8  the 
velocity  of  the  water.  Three  of  these  mills  are  in  one 
house,  at  Richmond,  Virginia — they  confirm  the  theory 
of  undershots,  being  very  good  mills. 

16.  Undershot.  Velocity  of  the  water  25,63  feet  per 
second,  velocity  of  the  wheel  19,05  feet,  being  more  than 
2-3.  Three  of  these  mills  are  in  one  house,  at  Peters- 
burg, in  Virginia — they  are  very  good  mills,  and  confirm 
the  theory.     See  art.  43. 

18.  Overshot  wheel.  Velocity  of  the  water  11,4  feet 
per  second,  velocity  of  the  wheel  10,96  feet,  nearly  as 
fast  as  the  water.  The  backs  of  the  buckets  strike  the 
water,  and  drive  a  gi'eat  part  over :  and  as  the  motion 
of  the  stone  is  about  right,  and  the  motion  of  the  wheel 
faster  than  assigned  by  the  theory,  it  shews  the  mill  to 
be  too  low  geared,  all  which  confirms  the  theory.  See 
art.  43. 

In  the  following  table  I  have  counted  the  diameter  of 
the  mean  circle  to  be  two-thirds  of  the  diameter  of  the 
great  circle  of  the  stone,  which  is  not  strictly  true.  The 
mean  circle  to  contain  half  the  area  of  any  other  circle 
must  be  ,707  parts  of  the  diameter  of  the  said  circle,  or 
nearly  ,7  or  2-3. 

Hence  the  following  theorem  for  finding  the  mean  cir- 
cle of  any  stone. 

THEOREM. 

Multiply  the  diameter  of  the  stone  by  ,707,  and  it  pro- 
duces the  diameter  of  the  mean  circle. 

EXAMPLE. 

Given,  the  diameter  of  the  stone  5  feet,  required  a 
mean  circle  that  shall  contain  half  its  area. 

Then,  5 x, 707=3,535  feet  the  diameter  of  the  mean 
circle. 


110  HYDRAULICS.  [Chap  12. 

ART.   63. 

FURTHER  OBSERVATIONS  ON  THE  FOLLOWING  TABLE. 

1.  The  mean  power  used  to  turn  the  5  feet  stones  in 
the  experiments  (No.  1.  7.  14.  17.)  is  87,5  cubochs  of 
the  measure  established  art.  6,  and  the  mean  velocity  is 
104  revolutions  of  the  stones  in  a  minute,  the  velocity  of 
the  mean  circle  being  18,37  feet  per  second,  and  their 
mean  quantity  ground  is  3,8lb.  per  minute,  which  is  3,8 
bushels  per  hour,  and  the  mean  power  used  to  each  foot 
of  the  area  of  the  stone  is  4,69  of  the  measure  aforesaid, 
done  by  36582  superficial  feet  passing  each  other  in  a 
minute.     Hence  we  may  conclude,  until  better  informed, 

1.  That  87,5  cubochs  of  power  per  second  will  turn 
a  5  feet  stone  104  revolutions  in  a  minute,  and  grind  3-8 
bushels  in  an  hour. 

2.  That  4,69  cubochs  of  power  is  required  to  every 
superficial  foot  of  a  mill-stone,  when  their  mean  circles 
move  with  a  velocity  of  18,37  feet  per  second.     Or, 

3.  That  for  every  36582  feet  of  the  face  of  stones  that 
pass  each  other  we  may  expect  3,81b.  will  be  ground, 
V  hen  the  stones,  grain,  Sec  are  in  the  state  and  condi- 
tion, as  were  the  above  stones  in  the  experiments. 


Chap.  12.] 


HYDRAULICS. 


Ill 


A  TABLE  OF  EXPERIMENTS  OP  EIGHTEEN  MILLS  IN  PRACTICE. 


JQuai.tily  ground  pt-r  mi- 
nute  in    pounds,  or  per 
liour  in  bushels.     .     . 

to  m 
CO  iji 

m 
N. 

co" 

in            m 

Superficial  feet  passed  in 
a  minute. 

to  lO 

t^<H 

36435 

35741 

108091 

in 

CO 

to 

CO 

in 

CO 

to 
CO 

95264 
49678 
39558 

74850 
35741 

Vi  locity  of  the  mean  cir- 
cle. 

01 

CO  to 

l>  00 

feto 

to  oo" 

O)  t^-* 
CO  oi  00 

oo  «>  t-I 

01 

CO 

00 

CO 

90 

oi  o>  CT  in       1^ 
Oj  00  ot)  f^_  o>  Oj 
to  to  oi  O  oi  N^ 

—   —  T-l  0-1   •-  -rH 

Power   required   to  each 
foot  of  face. 

05    Oi 

-4  in 

t^             m 

to             "_ 
■^           in 

Area  of  the  stones. 

a 

CO  OO 
to  -4 

oo  CO 

18.63 
18.63 
38.48 

CO 

36.63 
23.76 
18  63 

28.38 
18.63 

Diauieter  of  the  stone  in 
feet  and  inches. 

c 

CO  0«  00  tc  to  CO 

in  •*  •*  «}i  .5f  .*  <}i 

in  "rt  t^ 

m 

o 

m 

o 

»-  to         •*               .*  00 

tommintomtjit}! 

Revolutions  of  the  stones 
per  minute. 

J^  00 

ci  *  ©J  e»  tf  00  to 
a>  c»  o<  o)  o  o  •>» 

in  2  « 
o  o  t^ 

in 
O 

o 

in 

o 

-«oo~jico>nco.*to 
Koo-<— OTOOii-H 

R'luiids  in  the  trundles. 

in  «t  •+  -.+  -? 

-*  CO 

•*.*  CO 

—     T-l     01 

to 

to 

to 

aitotot^.-Hj'int© 

Cogs  iu  the  coiuiter  cog- 
wheel. 

.*  O?  -■♦  .*  -.-t  -*  00 

^:S 

.*  •*  .^                  .^  00   00 

•*  tji  m            «*  ■*  TT 

Rounds  in  the  wallowers. 

t^  c;»  -*.*•*  CO  o» 
•M  0»  0»  CM  OJ  01  51 

0>  01 
01  01 

m  K^  in            co  to  to 

01  01  oi          01  01  01 

Number  of    cogs  in   the 
master-wheel. 

00  00  o»       to 

00  00  !>.         to 

0» 

00  01  .# 
t--  t>  oo 

01 

oo 

•1! 

to        to  o  tf  to  01 
o       o  to  tf  to  t^ 

Velocity  of  the  circumfe- 
rence per  second. 

8.2 

8.5 

10.2 

9.3 

''     00? 

_o 

unloaded 

7  8 

8.8 
loatled 
unloaded 

IU 

-§  5 
11 

loaded 
unloaded 
loaded 
unloaded 
7.8 

9.1 

16.67 

19.05 

9.2 

10.96 

Number    of    revolutions 
per   minute. 

00  ci  CO        o» 

O  to  -*  o>  O  O  oo 
—  -"  01         —  01  01 

O  ti 

rs-" 

yx-  |>-\^                            in 

00  o  to  00       o  01  in  to  .* 
O)  -*  .n                  CO  -*■  —  -- 

Diameter  of  the  wheel. 

ti 

00  00  in       V) 

in 

to  to  to  in 

T-l    .-H    .-<   rt 

in 

in 

IT) 

oo           Oi  »H           ,^  r1 

Powei-  per  secon d ,  by  si  m- 
pl'-  theorem.     Art.  61. 

^ 

u 

to  N. 
l^  to 

01  o 

to           to 

00                  C> 

Cubic  feet  expended  per 
si  cnnd,  abating  for  fric- 
tion by  conjecture. 

3 

o 

00  in 

co'  CO 

oo  to 
in  to' 

in             o 

Velocity  of  the  water  per 
second,  by  theory. 

12.9 
11.17 
12.16 
14.4 

00 

CO 

C  O  CO 
N.  O)  tv. 
irj  -*  to 

16.2 

16.2 

24.3 

25.63 

14 

11.4 

\rvn  ot  the  gate,  abating 
f'  r  contraction  occasion- 
e'    by  friction. 

m  m 

00  01 

CO  CO 

in  'n 

CO  -^ 

to 
m 

HtK(l  above  the  centre  of 
the  gate. 

u 

to  31  0)         — 

oi  —  o»      CO 

CO 

CO 

oc  m 

0^   CO 

-*•<)•             CO  o» 

\  iruial   or    effective  de- 
scent of  the  water. 

t^ 

.'0. 
19  2 
16.2 

16.6 

m 
01 

en 

00  00 

b,    i^    -H 

W       in  lo       m 

o      —  o>'  o  oi 

-M        01        ii  — . 

dumber  of  Experiments. 

—  -■  -O       .* 

m 

'.O  t-,  X  Ci 

B, 

^ 

01 

CO       •«•  m  to  ■  ~  00 

In  the  ."d,  4th,  13ih  and  18th  experiments,  in  the  above  table,  there  are  two  pair  of  stones  to 
one  water-wheel,  the  gears,  &c.  of  which  are  shewn  by  the  braces.  If  the  reader  will  by  a  rate 
araw  small  lines  between  the  experiments,  the  table  will  be  easiar  read. 


112  HYDRAULICS.  [Chap.  12, 

OBSERVATIONS  CONTINUED  FROM  PAGE  110. 

But  as  we  cannot  attain  to  a  mathematical  exactness 
in  those  cases,  and  as  it  is  evident  that  all  the  stones  in 
the  said  experiments  have  been  working  with  too  little 
power,  because  it  is  known  that  a  pair  of  good  burr 
stones  of  5  feet  diameter,  will  grind  sufficiently  well 
about  125  bushels  in  24?  hours  ;  that  is  5,3  bushels  in 
an  hour,  which  would  require  6,4  power  per  second — 
we  may  say  6  cubochs  per  second,  when  5  feet  stones 
grind  5  bushels  per  hour,  for  the  sake  of  simplicity. 
Hence  we  deduce  the  following  simple  theorem  for  de- 
termining the  size  of  the  stones  to  suit  the  power  of  any 
given  seat,  or  the  power  required  to  any  size  of  a  stone. 

THEOREM. 

Find  the  power  by  the  theorem  in  art.  6 1  ;  then  divide 
the  power  by  6,  which  is  the  power  required,  by  1  foot, 
and  it  will  give  you  the  area  of  the  stone  that  the  power 
will  drive,  to  which  add  1  foot  for  the  eye,  and  divide 
by  ,7854,  and  the  quotient  will  be  the  square  of  the  dia- 
meter :  or,  if  the  power  be  great,  divide  by  the  product 
of  the  area  of  any  size  stones  you  choose,  multiplied  by 
6,  and  the  quotient  will  be  the  number  of  stones  the 
power  will  drive  :  or,  if  the  size  of  the  stone  be  given, 
multiply  the  area  by  6  cubochs,  and  the  product  is  the 
power  required  to  drive  it. 

EXAMPLES. 

1.  Given,  9  cubic  feet  per  second,  12  feet  perpendi- 
cular, virtual,  or  effective  descent,  required  the  diame- 
ter of  the  stone  suitable  thereto. 

Then,  by  art.  61,  9xl2=i08,  the  power,  and 
108  I  6=18,  the  area,  and  18x1  |  ,785-l-=2+,3  the  root 
of  which  is  4,9  feet,  the  diameter  of  the  stone  required. 

Observation  5th.  The  velocities  of  the  mean  circles 
of  these  stones  in  the  table  are  some  below  and  some 
above  18  feet  per  second,  the  mean  of  them  all  being 
nearly  18  feet;  therefore  I  conclude  that  18  feet  per 
second  is  a  good  velocity  in  general,  for  the  mean  circle 
of  any  sized  stone. 


Chap.  12.]  HYDRAULICS.  113 

Of  the  different  quantity  of  Surfaces  that  are  passed  by 
AlHl-stones  of  different  diameters  with  different  velo- 
cities. 

Supposing  the  quantity  ground  by  mill-stones  and 
power  required  to  turn  them  to  be  as  the  passing  sur- 
faces of  their  faces,  each  superficial  foot  that  passes  over 
another  foot  requires  a  certain  power  to  grind  a  certain 
quantity  :  Then  to  explain  this  let  us  premise, 

1.  The  circumference  and  diameter  of  circles  are 
directly  proportional.  That  is,  a  double  diameter  gives 
a  double  circumference. 

2.  The  areas  of  circles  are  as  the  squares  of  their  dia- 
meters. That  is,  a  double  diameter  gives  4  times  the 
area. 

3.  The  square  of  the  diameter  of  a  circle  multiplied 
by  ,7854  gives  its  area. 

4.  The  square  of  the  area  of  a  mill  stone  multiplied 
by  its  number  of  revolutions,  gives  the  surface  passed. 
Consequently, 

5.  Stones  of  unequal  diameters  revolving  in  equal 
times.  Their  passing  surfaces,  quantity  ground,  and 
power  required  to  drive  them,  aa  ill  be  as  the  squares  of 
their  areas,  or  as  the  biquadrate  of  their  diameters.  That 
is,  a  double  diameter  will  pass  16  times  the  surface.* 

6.  If  the  velocity  of  their  mean  circles  or  circumfe- 
rences be  equal  their  passing  surfaces,  quantity  ground, 
and  power  required  to  move  them,  will  be  as  the  cubes 
of  their  diameters.f 

7.  If  the  diameters  and  velocities,  be  unequal,  their 
passing  surfaces  and  quantity  ground,  &c.  will  be  as  the 
squares  of  their  areas,  multiplied  by  their  revolutions. 

8.  If  their  diameters  be  equal  the  quantity  of  sur- 
faces passed,  &c.  are  as  their  velocities  or  revolutions 
simply. 

•  The  diameter  of  a  4  feet  stone  squared,  multiplied  by  ,7854  equal 
12,56  its  area;  which  squared  is  \57,75  feet,  the  surface  passed  at  one  re- 
volution :  and  8  multiplied  by  8  equal  64,  which  m\iltiplied  by  .7854  equal 
50,24  being  the  area  of  an  8  feet  stone  ;  which  squared  is  2524,04  the  sur- 
face passed,  which  surfaces  are  as  1  to  16. 

t  Because  the  8  feet  stone  will  revolve  only  half  as  of»en  as  the  4  feet, 
therefore  their  quantity  of  surface  pussed,  &.c.  can  only  be  half  as  much 
more  as  it  was  in  the  last  case ;  that  is,  as  8  to  1- 

r 


114  HYDRAULICS.  [Chap.  12, 

But  we  have  been  supposing  theory  and  practice  to 
a^ee  strictly,  which  they  will  by  no  means  do  in  this 
case.  The  quantit)*  ground  and  power  used  by  large 
stones  more  than  by  small  ones  will  not  be  in  the  ratio 
assigned  by  the  theory;  because  the  meal  having  to 
pass  a  greater  distance  through  the  stone,  is  operated 
upon  oftener,  which  operations  must  be  lighter,  else  it 
will  be  overdone ;  by  which  means  large  stones  may 
grind  equal  quantities  with  small  ones,  and  with  equal 
power,  and  do  it  with  less  pressure  ;  therefore  the  flour 
will  be  better.*     See  art.  HI. 

From  these  considerations,  added  to  experiments,  I 
conclude,  that  the  po\Aer  required  and  quantity  ground, 
will  nearer  approach  to  be  as  the  area  of  the  stones, 
multiplied  into  the  velocity  of  the  mean  circles ;  or, 
which  is  nearly  the  same,  as  the  squares  of  their  dia- 
meters. But  if  the  velocities  of  their  mean  circles  or 
circumferences  be  equal,  then  it  will  be  as  their  area, 
simply. 

On  these  principles  I  have  calculated  the  following 
table,  shewing  the  power  req  ured  and  quantity  ground 
both  by  theory  and  what  I  suppose  to  be  the  nearest 
practice. 

*  A  French  author  (M.  Pabre)  says,  that  by  experiments  he  has  found, 
that  to  produce  the  bMt  flour,  a  stone  5  feet  diameter  should  revolve  be- 
tween 48  and  61  times  in  a  minute.  This  is  much  slower  than  prartice  in 
America,  but  we  may  conclude  that  it  is  best  to  err  on  the  side  of  slower 
than  faster  than  common  practice;  especially  when  the  power  is  too  small 
for  the  size  of  the  stone- 


Chap.  12.] 


HYDRAULICS. 


115 


A  TABLE 


AREA  OF  MILL  STONES, 


DIFFERENT  DIAMETERS, 

Deducting  1  foot  for  the  eye;  and  of  'he  power  required  to  move  them 
with  a  mean  velocity  of  18  feet  per  second,  8ic. 


o 

> 

"V 

0 

^ 

2; 

*o 

■V 

fi 

45 

3 

rt 

n 

o 
-«» 

cr 
n 

V- 

ft 

o 

"*> 

s- 
n 

>-'  o 

0  n  <i 

0 

c 

3 

a' 

-;? 
^3 

< 

It 

0     3" 

3  °"3 

3  n>   3 

"'^  =  't 

^      W      -T 

0 
ft 

ri 
—  ft 

fo  j:i 

".    c 

°  5 

->i  (t 

"  pi 

»  at; 

0  3 
^  c 

C.  3 

p  w  S 
■a  c  S 

ft     8=     -• 
•^    ft  ^^ 

5  2,1 
0  zi  = 
0  s  = 

O 

3 
'0 

o  — 

'^  3 
"»   fl 

2  S 

0  5 

='3   3' 
fl   1)   n 

»  2 

0  •5 

3  -0 
ft    0 

ft    5  "O 

5' 

l-f  "^ 

_.  ro   ft 

S.3 

-^tt 

1-5-^" 

"     r^XI 

i.  3' 

^    05 

ft     ft     X 

n 

3 

ft   C- 

3^ 
:3 

8=    !f 

ft     -♦    ft 

■    0-3 

ft  ^ 

^  0 

ft     ■" 

2  2>=^ 

■o 

•      "1 

0   '^ 

5'  ^' 

7q    3- 

0  0 

0 
0 

c 

-■  3 
o_  3 

It,   .-^ 

ft   0   C 
c  M  r. 

^£ 

3   a- 

ft 

3     -■ 

-a 
ft    tft 

-    CO    0 

3' 

Ch3 

=  i 

3 

00 

."11 

3  I 

^1 

3 
c 
3 

—  -  w 

3    -*    m 

3,5 

s.      t 

cuhs. 

fet-.. 

sup    f 

lbs. 
1,49 

cuhs. 

lbs. 

Ihs. 

8,62 

51.72 

7,777 

138,8 

10312 

33,1 

2.3 

2.45 

3.75 

9,99 

59,94 

2,8 

4, 

11,56 

69,36 

8,888 

121,5 

16236 

2,3 

52 

3,1 

3.2 

4.25 

13,18 

79, 

3,6 

4.5 

14,9 

89,4 

9,99 

108,1 

23999 

3,46 

77 

4, 

4,05 

4,75 

16,71 

100,26 

4,5 

5, 

18,63  111,78 

11,09 

97,4 

34804 

5, 

111,78 

5, 

5, 

5,25 

20,64;  123,84 

5,53 

5,5 

22,76  136,5  | 

6,05 

5,75 

24,96 

153,7 

6.6 

6. 

27,27 

163,6 

13,37 

80,7 

60012 

8,6 

192 

7,3 

7,2 

6,25 

29,67 

178. 

7.8 

6,5 

32,18 

196, 

8,4 

6.75 

34,77 

208,6 

9,1 

7, 

37  48 

225, 

15,55 

69,4 

97499 

14,06 

313 

10 

9,8 

1 

2 

3 

4 

5 

6 

4 

8 

9 

10 

Note.  The  reason  why  the  quantity  ground  in  the  7th  column,  is  not 
exactly  as  the  cubes  of  the  diameter  of  the  stone,  and  m  the  9ih  column 
not  exactly  as  the  squares  of  its  diameter,  is  the  deduction  for  the  eye,  be- 
ing equal  in  each  stone,  destroys  the  proportion. 

The  engine  of  a  paper-mill,  roll  2  feet  diameter,  2  feet  long,  revolving 
160  tiroes  in  a  minute,  requires  equal  power  with  a  4  feet  stone,  grinding 
5  bushels  an  hour. 


116  HYDRAULICS.  [Chap.  12. 

Having  now  laid  down  in  art.  61,  62,  and  63,  a  theory 
for  measuring  the  power  of  any  mill-scat,  and  for  ascer- 
taining the  quantity  of  that  power  that  mill-stones  of 
different  diameters  will  require,  by  which  we  can  find 
the  diameter  of  the  stones  to  suit  the  power  of  the  seat : 
and  having  fixed  on  six  cubochs  of  that  power  per  se- 
cond to  every  superficial  foot  of  the  mill- stone,  as  re- 
quisite to  move  the  mean  circle  of  the  stone  18  feet  per 
second,  when  in  the  act  of  grinding  with  moderate  and 
sufficient  feed,  and  having  allowed  the  passing  of  34804 
feet  per  minute  to  grind  51b.  in  the  same  time,  which  is 
the  effect  of  the  five  feet  stone  in  the  table,  by  which,  if 
right,  we  can  calculate  the  quantity  that  a  stone  of  any 
size  will  grind  with  any  velocity. 

I  have  chosen  a  velocity  of  18  feet  per  second,  for  the 
mean  circle  of  all  stones,  which  is  slower  than  common 
practice,  but  not  too  slow  for  making  good  flour.  See 
art.  111.  Here  will  appear  the  advantage  of  large  stones 
over  small  ones;  for  if  we  will  make  small  stones  grind 
as  fast  as  large  ones,  we  must  give  them  such  velocity  as 
to  heat  the  meal. 

But  I  wish  to  inform  the  reader,  that  the  experiments, 
from  which  I  have  deduced  the  quantity  of  power  to 
each  superficial  foot  to  be  six  cubochs,  have  not  been 
sufficiently  accurate  to  be  relied  on ;  but  it  will  be  easy 
for  every  ingenious  mill-'wright  to  make  accurate  experi- 
ments to  satisfy  himself  as  to  this.*- 

*  After  having'  pablished  the  fist  edition  of  lliis  work,  I  have  been  in- 
formed, that  by  accurate  experiments  made  at  the  expense  of  the  British 
j^overnment,  it  was  ascertained  that  the  power  produced  by  40,000  cubic 
feet  of  water  descending^  1  foot,  will  j^rind  and  bolt  1  bushel  of  wheat.  If 
this  be  true,  then,  to  find  the  quantity  that  any  sii-eatn  will  grind  per  hour, 
xnuliiply  the  cubic  feet  of  waf^r  that  it  affords  per  hoiu-,  by  the  virtual  de- 
scent, (that  is,  half  of  the  head  above  the  wiieel  added  to  the  fall  after  it 
enters  an  overshot  wheel,)  and  divide  tiiat  product  by  40,000,  and  the  quo- 
tient is  the  answer  in  bushels  per  hour  that  the  stream  w  dl  grind. 

EXAMPLE. 

Suppose  a  streant  affords  32,000  cubic  feet  water  per  hour,  and  the  total 
fall  19, .;8  feet  ;  then  by  the  tisbie  for  overshot  mills,  art  •  73,  the  wheel 
shotilfl  be  16  ftet  diameter,  head  above  the  wheel,  3,28  feet.  Then  half 
3,28  =  1,64.  which  added  to  16=1764  feet  virtual  descent,  and  17,64x 
32000 =.5 63480,  which  drvlded  by  40,000,  quotes  14,08  bushels  per  hour 
"the  stream  will  grind. 


Chap.  12.]  HYDRAULICS.  lit 

ART.    64. 

OF  CANALS  FOR  CONVEYING  WATER  TO  MILLS. 

In  digging  canals  we  must  consider  that  water  will 
come  to  a  level  on  its  surface,  be  the  form  of  the  bottom 
as  it  may.  If  we  have  once  determined  on  the  area 
of  the  section  of  the  canal  necessary  to  convey  a 
sufficient  quantity  of  water  to  the  mill,  we  need  only 
mind  to  keep  to  that  area  in  the  whole  distance,  and 
need  not  pay  much  regard  to  the  depth  or  width,  if  there 
be  rocks  in  the  way.  Much  expense  may  be  oftentimes 
saved,  by  making  the  canal  deep  where  it  cannot  easily 
be  got  wide  enough,  and  wide  where  it  cannot  easily  be 
got  deep  enough.  Thus,  suppose  we  have  determined 
it  to  be  4  feet  deep,  and  6  feet  wide,  then  the  area  of  its 
section  will  be  24. — Let  fig.  36,  plate  IV.  represent  a 
canal,  the  line  A  B  the  level  or  surface  of  the  water, 
C  D  the  side,  E  F  the  bottom,  A  C  the  width  6  feet, 
A  E  the  depth  4  feet.  Then,  if  there  be  rocks  at  G,  so 
that  we  cannot  without  great  expense  obtain  more  than 
3  feet  width,  but  8  feet  clepth  at  a  small  expense :  then 
8x3=24,  the  section  required.  Again,  suppose  a  fiat 
rock  to  be  at  H,  so  that  we  cannot,  without  great  ex- 
pense, obtain  more  than  2  feet  depth,  but  can,  with  small 
expense,  obtain  12  feet  width:  then  2x12=24,  the  sec- 
tion required ;  and  the  water  will  come  on  equally  well, 
even  if  it  were  not  more  than  ,5  of  a  foot  deep,  provided 
it  be  proportionably  wide.  One  disadvantage  however 
arises  in  having  canals  too  shallow  in  places,  because 
the  water  in  dry  seasons,  may  be  too  low  to  rise  over 
them;  but  if  the  water  was  always  to  be  of  one  height, 
the  disadvantage  would  be  but  little.  The  current  will 
keep  the  deep  places  open ;  light  sand  or  mud  will  not 
settle  in  them.  This  will  seem  paradoxical  to  some, 
but,  seeing  the  experiment  may  be  a  saving  of  expense, 
it  may  be  worth  trying. 


118  HYDRAULICS.  [Chap.  12. 

ART.   65, 

OF  THE  SIZE  AND  FALL  OF  CANALS, 

As  to  the  size  and  fall  necessary  to  convey  any  quan- 
tity of  water  required  to  a  mill,  I  do  not  find  any  rule 
laid  down  for  either.  But  in  order  to  establish  one,  let 
us  consider,  that  the  size  depends  entirely  upon  the 
quantity  of  water  and  the  velocity  with  which  it  is  to 
pass:  therefore,  if  we  can  determine  on  the  velocity, 
which  I  will  suppose  to  be  from  1  to  2  feet  per  second 
— but  the  slower  the  better,  as  there  will  be  the  less  fall 
lost — we  can  find  the  size  of  the  canal  by  the  following 

THEOREM. 

Divide  the  quantity  required  in  cubic  feet  per  second, 
by  the  velocity  in  feet  per  second,  and  the  quotient  will 
be  the  area  of  the  section  of  the  canal.  Divide  that  area 
by  the  proposed  depth,  and  the  quotient  is  the  width : 
or,  divide  by  the  width,  and  the  quotient  is  the  depth. 

PROBLEM  L 

Given,  a  5  feet  mill-stone  to  be  moved  18  feet  per 
second,  velocity  of  its  mean  circle  on  a  seat  of  10  feet 
virtual  or  effective  descent,  required  the  size  of  the  canal, 
with  a  velocity  of  1  foot  per  second. 

Then,  by  theorem  in  art.  63  :  The  area  of  the  stone 
18,63  feet,  multiplied  by  six  cubochs  of  power,  is  equal 
111,78  cubochs  for  the  power  (in  common  practice  say 
113  cubochs)  which,  divided  by  10  the  fall,  quotes 
11,178  cubic  feet  required  per  second,  which,  divided 
by  1,  the  velocity  proposed  per  second,  quotes  11,178 
feet,  the  area  of  the  section,  which  divided  by  the  depth 
proposed,  two  feet,  quotes  5,58  feet  for  the  width. 

PROBLEM  IL 

Given,  a  mill-stone  6  feet  diameter,  to  be  moved  with 
a  velocity*of  18  feet  per  second  of  its  mean  circle,  to  be 
turned  by  an  undershot  wheel  on  a  seat  of  8  feet  per- 


Ghap.l2.]  HYDRAULICS.  119 

pendicular  descent,  required  the  power  necessary  per 
second  to  drive  them,  and  the  quantity  of  water  per  se- 
cond to  produce  said  power,  likewise  the  size  of  the 
canal  to  convey  the  water  with  a  velocity  of  1,5  feet  per 
second. 

Then,  by  art.  61,  8  feet  perpendicular  descent,  on  the 
undershot  principle,  is  only=4  feet  virtual  or  effective 
descent :  and  the  area  of  the  stone  by  the  table  (art.  63) 
=27,27  feetx6  cubochs=l63,62  cubochs,  for  the  power 
per  second,  which  divided  by  4,  the  effective  descent= 
40,9  cubic  feet,  the  quantity  required  per  second,  which 
divided  by  the  velocity  proposed  1,5  feet  per  second= 
20,45,  for  the  area  of  the  section  of  the  canal,  which  di- 
vided by  2,25  feet,  the  depth  of  the  canal  proposed=9,l 
feet,  the  width.* 

As  to  the  fall  necessar}^  in  the  canal,  I  may  observe, 
that  the  fall  should  be  in  the  bottom  of  the  canal  and 
none  on  the  top,  which  should  be  all  the  way  on  a  level 
■with  the  water  in  the  dam,  in  order  that  when  the  gate 
is  shut  down  at  the  mill,  the  water  will  not  overflow  the 
banks,  but  stand  at  a  level  with  the  water  in  the  dam ; 
that  is,  as  much  fall  as  there  is  to  be  in  the  whole  length 
of  the  canal,  so  much  deeper  must  the  canal  be  at  the 
mill  than  at  the  dam.  From  observations  I  conclude 
that  about  3  inches  to  100  yards  will  be  sufficient,  if 
the  canal  be  long,  but  more  will  be  better  if  it  be  short, 
and  the  head  apt  to  run  down  when  water  is  scarce,  for 
the  shallower  the  water  the  greater  must  be  the  velocity, 
and  more  fall  is  required. — A  French  author,  M.  Fabre, 
allovAS  1  inch  to ^00  feet. 

»  An  acre  of  a  mill-pond  contains  43560  cubic  feet  of  water,  for  every 
foot  of  its  depth. 

Suppose  your  pond  contains  3  acres  and  is  3  feet  deep,  then  43560,  mul- 
tiplied by  3,  is  equi*l  130680,  which  multiplied  by  3,  is  equal  392040  cubic 
feet,  its  contents,  which  vided  bv  the  cubic  feet  your  mill  uses  per  se- 
conn  (say  10)  is  equal  39204  seconds,  or  10  hours,  the  time  the  pond  will 
keep  the  mill  going. 


120  HYDRAULICS.  [Chap.12. 

ART.    66. 

OF  AIR  PIPES  TO  PREVENT  TIGHT  TRUNKS  FROM  BURSTING 
WHEN  FILLED  WITH  WATER 

When  water  is  to  be  conveyed  under  ground,  or  in  a 
tight  trunk  below  the  surface  of  the  water  in  the  reser- 
voir, to  any  considerable  length,  there  must  be  air-pipes 
(as  they  have  been  called)  to  prevent  the  trunk  from 
bursting.  To  understand  their  use  let  us  suppose  a 
trunk  100  feet  long,  16  feet  below  the  surface  of  the 
water,  to  fill  which  draw  a  gate  at  one  end  of  equal  size 
with  the  trunk.  Then  the  water,  in  passing  to  the  other 
end  acquires  great  velocity  if  it  meets  no  resistance,  which 
velocity  is  suddenly  to  be  stopped  when  the  ti'unk  is  full. 
This  great  column  of  water  in  motion,  in  this  case,  would 
strike  with  a  force  equal  to  a  solid  body  of  equal  weight 
and  velocity,  the  shock  of  which  would  be  sufficient  to 
burst  any  trunk  that  ever  was  made  of  ^vood.  Many 
having  thought  the  use  of  these  pipes  to  be  to  let  out  the 
air,  have  made  them  too  small,  so  that  they  would  vent 
the  air  fast  enough  to  let  the  water  in  u  ith  considerable 
velocity,  but  would  not  vent  the  water  fast  enough  when 
full,  to  check  its  motion  easily,  in  which  case  they  are 
worse  than  none  at  all,  for  if  the  air  cannot  escape  freely, 
the  water  cannot  enter  freely. 

Whenever  the  air  has  been  compressed  in  the  trunk 
by  the  water  coming  in,  it  has  made  a  great  blowing 
noise  in  escaping  through  the  crevices,  and  therefore  has 
been  blamed  as  the  cause  of  the  bursting  of  the  trunk ; 
whereas  it  acted  by  its  elastic  principle^  as  a  great  pre- 
ventive against  it.  For  I  do  suppose,  that  if  we  were 
to  pump  the  air  all  out  of  a  trunk,  100  feet  long,  and  3 
by  3  feet  wide,  and  let  the  water  in  with  full  force,  that 
it  would  burst,  if  as  thick  as  a  cannon  of  cast  metal :  be- 
cause in  that  case  there  would  be  900  cubic  feet  of  water, 
equal  to  562501bs.  pressed  on  by  the  weight  of  the  at- 
mosphere, with  a  velocity  of  47  feet  per  second,  to  be 
suddenly  stopped,  the  shock  would  be  inconceivable. 

*  To  prevent  ice  from  gatlieringf  on  overshot  wheels  when  standing',  the 
water  is  shut  out  of  the  trunk  by  a  pate  at  the  ranal,  and  what  Iciks 
throuf^h  it  is  let  through  a  hole  in  the  bottom  of  the  trunk  ;  the  water  is  let 
in  again  with  full  force- 


Chap.  12.}  HYDRAULICS.  121 

Therefore  I  do  conclude  it  best,  to  make  an  air- pipe 
for  every  30  or  30  feet,  of  the  full  size  of  the  trunk  ; 
but  this  will  depend  much  on  the  depth  of  the  trunk 
below  the  surface  of  the  reservoir,  and  many  other  cir- 
cumstances. 

Having  now  said  what  was  necessary,  in  order  the 
better  to  understand  the  theory  of  the  power  and  prin- 
ciples of  mechanical  engines,  and  water  acting  on  the 
different  principles  on  water-wheels,  and  for  the  esta- 
blishing new  and  true  theories  of  the  motion  of  the  dif- 
ferent kinds  of  water-wheels,  I  here  quote  many  of  the 
ingenious  Smeaton's  experiments,  that  the  reader  may 
compare  them  with  the  theories  established,  and  judge 
for  himself. 


ART.    67. 

SMEATON'S  EXPERIMENTS. 

.4?i  experimental  Enquky^  read  in  the^^hilosophical  So- 
ciety in  London^  May  3c/,  and  lOtkj  1759,  concerning 
the  Natural  Powers  of  Water  to  turn  Mills  and  other 
Machines,  depending  on  a  circular  motion,  by  James 
Smeaton,  F.  R.  S. 

What  I  have  to  communicate  on  this  subject  was 
originally  deduced  from  experiments  made  on  working 
models,  which  I  look  upon  as  the  best  means  of  obtain- 
ing the  outlines  in  mechanical  enquiries.  But  in  this 
case  it  is  necessary  to  distinguish  the  circumstances  in 
which  a  model  differs  from  a  machine  in  large  :  other- 
wise a  model  is  more  apt  to  lead  us  from  the  truth  than 
towards  it.  Hence  the  common  observation,  that  a 
thing  may  do  very  well  in  a  model  that  will  not  do  in 
large.  And  indeed  though  die  utmost  circumspection 
be  used  in  this  way,  the  best  structure  of  machines  can- 
not be  fully  ascertained,  but  by  making  trials  w  ith  them 
of  their  proper  size.  It  is  for  this  purpose  that  though 
the  models  referred  to,  and  the  greatest  part  of  the  fol- 
lowing experiments,  were  made  in  the  years  1752,  and 
1753,  yet  I  deferred  offering  them  to  the  society  till  I  had 
an  opjx)rtunity  of  putting  the  deduction  made  Xherefrom  in 


122  HYDRAULICS.  [Chap.  12. 

real  practice,  in  a  variety  of  cases  and  for  various  pur- 
poses, so  as  to  be  able  to  assure  the  society,  that  I  have 
found  them  to  answer. 

PART  I. 

CONCERNING    UNDERSHOT    WATER-WHEELS. 

Plate  XII.  is  a  view  of  the  machine  for  experiments, 
on  water-wheels,  wherein 

ABCD  is  the  lower  cistern  or  magazine  for  receiving 
the  water  after  it  has  left  the  wheel,  and  for  supplying 

DE  the  upper  cistern  or  head,  wherein  the  water  be- 
ing raised  to  any  height  by  a  pump,  that  height  is  shewn 

FG  a  small  rod  divided  into  inches  and  parts,  with  a 
float  at  the  bottom  to  move  the  rod  up  and  down,  as  the 
surface  of  the  water  rises  and  falls. 

HI  is  a  rod  by  which  the  sluice  is  drawn,  and  stopped 
at  any  height  required,  by  means  of 

K  a  pin  or  peg,  which  fits  several  holes  placed  in  the 
manner  of  a  diagonal  scale  upon  the  face  of  the  rod  HI. 

GL  ^  the  upper  part  of  the  rod  of  the  pump  for  draw- 
ing the  water  out  of  the  lower  cistern,  in  order  to  raise 
and  keep  up  the  surface  thereof  to  its  desired  height  in 
the  head  DE,  thereby  to  supply  the  w'ater  expended  bj 
the  aperture  of  the  sluice. 

MM  is  the  arch  and  handle  of  the  pump,  which  is 
limited  in  its  stroke  by 

N  a  piece  for  stopping  the  handle  from  raising  the 
piston  too  high,  that  also  being  prevented  from  going  too 
low,  by  meeting  the  bottom  of  the  barrel. 

O  is  the  cylinder  upon  which  the  cord  winds,  and 
which  being  conducted  over  the  pullies  P  and  Q,  raises. 

R  the  scale,  into  which  the  weights  are  put  for  trying 
the  power  of  the  water. 

W  the  beam,  which  supports  the  scale  that  is  placed 
15  or  16  feet  higher  than  the  wheel. 

XX  is  the  pump-barrel  5  inches  diameter  and  11 
inches  long. 

Y  is  the  piston,  and 

Z  is  the  fixed  valve. 


Chap.  12.]  HYDRAULICS.  123 

GV  is  a  cylinder  of  wood  fixed  upon  the  pump-rod, 
and  reaches  above  the  surface  of  the  water;  this  piece  of 
wood  being  of  such  a  thickness  that  its  section  is  half  the 
area  of  the  pump-barrel,  will  cause  the  water  to  rise  in 
the  head  as  much  while  the  piston  is  descendin^as  while 
it  is  rising,  and  will  thereby  keep  the  gauge-rod  FG  more 
equally  to  its  height. 

a  a  shews  one  of  the  two  wires  that  serves  as  a  direc- 
tor to  the  float. 

b  is  the  aperture  of  the  sluice. 

c  a  is  a  cant-board  for  canting  the  water  down  the  open- 
ing c  d  into  the  lower  cistern. 

c  e  is  a  sloping  board  for  bringing  back  the  water  that 
is  thrown  up  by  the  wheel. 

There  is  a  contrivance  for  engaging  and  disengaging 
the  scale  and  weight  instantaneously  from  the  wheel,  by 
means  of  a  hollow  cylinder  on  which  the  cord  winds  by 
slipping  it  on  the  shaft,  and  when  it  is  disengaged  it  is 
held  to  its  place  by  a  ratchet-wheel,  for  without  this, 
experiments  could  not  be  made  with  any  degree  of  ex- 
actness. 

The  apparatus  being  now  explained,  I  think  it  neces- 
sary to  assign  the  sense  in  which  I  use  the  term  power. 

The  word  power  is  used  in  practical  mechanics,  I  ap- 
prehend, to  signify  the  exertion  of  strength,  gravity,  im- 
pulse, or  pressure,  so  as  to  produce  motion. 

The  raising  of  a  weight  relative  to  the  height,  to 
which  it  can  be  raised  in  a  given  time,  is  the  most  pro- 
per measure  of  power.  Or  in  other  words,  if  the  weight 
raised,  is  multiplied  by  the  height  to  which  it  can  be 
raised  in  a  given  time,  the  product  is  the  measure  of  the 
power  raising  it,  and  consequently  all  those  powers  are 
equal.  But  note  all  this  is  to  be  understood  in  case  of 
slow  or  equable  motion  of  the  body  raised,  for  in  quick, 
accelerated,  or  retarded  motions,  the  vis  inertia  of  the  mat- 
ter moved  will  make  a  variation. 

In  comparing  the  eflTects  procuced  by  water-wheels 
with  the  powers  producing  them  ;  or  in  other  words,  to 
know  what  part  of  the  original  power  is  necessarily  lost 
in  the  application,  we  must  previously  know  how  much 
of  the  power  is  spent  in  overcoming  the  friction  of  the 


134  HYDRAULICS.  [Chap.  12, 

machinery  and  the  resistance  of  the  air,  also  what  is  the 
real  velocity  of  the  water  at  the  instant  it  strikes  the 
wheel,  and  the  real  quantity  of  water  expended  in  a 
given  time. 

From  the  velocity  of  the  water  at  the  instant  that  it 
strikes  the  w^heel,  given ;  the  height  of  the  head  produc- 
tive of  such  velocity  can  be  deduced,  from  acknow^- 
ledged  and  experienced  principles  of  hydrostatics  :  so 
that  by  multiplying  the  quantity  or  weight  of  water 
really  expended  in  a  given  time,  by  the  height  of  head 
so  obtained ;  which  must  be  considered  as  the  height 
from  which  that  weight  of  water  had  descended,  in  that 
given  time ;  we  shall  have  a  product  equal  to  the  origi- 
nal power  of  the  water,  and  clear  of  all  uncertainty  that 
would  arise  from  the  friction  of  the  water  in  passing 
small  apertures,  and  from  all  doubts,  arising  from  the 
different  measure  of  spouting  waters,  assigned  by  differ- 
ent authors. 

On  the  other  hand  the  sum  of  the  weights  raised  by 
the  action  of  this  water,  and  of  the  weight  required  to 
overcome  the  friction  and  resistance  of  the  machine  ; 
multiplied  by  the  height  to  which  the  weight  can  be  raised 
in  the  time  given,  the  product  will  be  the  effect  of  that 
power  ;  and  the  proportion  of  the  two  products  will  be  the 
proj:)ortion  of  the  pow  er  to  the  effect :  so  that  by  loading 
the  wheel  with  different  weights  successively,  we  shall  be 
able  to  determine  at  what  particular  load  and  velocity  of 
the  wheel  the  effect  is  a  maximum. 
To   determine  the  Velocity  of  the   Water  striking  the 

Wheel. 

Firt  let  the  wheel  be  put  in  motion  by  the  water,  but 
without  any  weight  in  the  scale  ;  and  let  the  number  of 
turns  in  a  minute  be  60  :  now  it  is  evident,  that  was  the 
wheel  free  from  friction  and  resistance,  that  60  times  the 
circumference  of  the  wheel  would  be  the  space  through 
which  the  water  would  have  passed  in  a  minute ;  with 
that  velocily  wherewith  it  struck  the  wheel :  But  the 
wheel  being  incumbered  with  friction  and  resistance, 
and  )'et  moving  60  turns  in  a  minute,  it  is  plain  that  the 
velocity  of  the  water  must  have  been  greater  than  60 
circumferences,  before  it  met  with  the  wheel.     Let  the 


Chap.  1:2.]  HYDRAULICS.  125 

cord  now  be  wound  round  the  cylinder,  but  contrary  to 
the  usual  way,  and  put  as  much  weight  in  the  scale  as 
will  \vithout  any  water  turn  the  wheel  somewhat  faster 
than  60  turns  in  a  minute,  suppose  63,  and  call  this  the 
counter-weight,  then  let  it  be  tried  again  with  the  water 
assisted  by  this  counter-weight,  the  wheel  therefore  will 
now  make  more  than  60  turns  in  a  minute,  suppose  6'1<, 
hence  we  conclude  the  water  still  exerts  some  power  to 
turn  the  wheel.  Let  the  weight  be  increased  so  as  to 
make  64^  turns  in  a  minute  without  the  w^ater,  then  try 
it  with  the  water  and  the  weight  as  before,  and  suppose 
it  now  makes  the  same  number  of  turns  with  the  water, 
as  without,  viz.  64|,  hence  it  is  evident,  that  in  this  case 
the  wheel  makes  the  same  number  of  turns  as  it  would 
with  the  water,  if  the  wheel  had  no  friction  or  resistance 
at  all,  because  the  weight  is  equivalent  thereto,  for  if  the 
counter-weight  was  too  little  to  overcome  the  friction, 
the  water  would  accelerate  the  wheel,  and  if  too  great  it 
would  retard  it,  for  the  water  in  this  case  becomes  a 
regulator  of  the  wheel's  motion,  and  the  velocity  of  its 
circumference  becomes  a  measure  of  the  velocity  of  the 
water. 

Li  like  manner  in  seeking  the  greatest  product  or 
maximum  of  effect;  having  found  by  trials  what  weight 
gives  the  greatest  product,  by  simply  multiplying  the 
weight  in  the  scale,  by  the  number  of  turns  of  the  wheel, 
find  what  weight  in  the  scale,  when  the  cord  is  on  the 
contrary  side  of  the  cylinder,  will  cause  the  wheel  to 
make  the  same  number  of  turns,  the  same  way  without 
water;  it  is  evident  that  this  weight  will  be  nearly  equal 
to  all  friction  and  resistance  taken  together;  and  con- 
sequently that  the  weight  in  the  scale,  with  twice*  the 
weight  of  the  scale,  added  to  the  back  or  counter- weight, 
will  be  equal  to  the  weight  that  could  have  been  raised 
supposing  the  machine  had  been  without  friction  or  re- 
sistance, and  which  multiplied  by  the  height  to  which  it 
was  raised,  the  product  will  be  the  greatest  effect  of  that 
power. 

•  The  weight  of  the  scale  makes  part  of  the  weight  both  ways,  viz.  both 
ef  the  weight  and  counter-weight- 


80 


126  HYDRAULICS.  [Chap.  12. 

The  Quantity  of  IVater  expended  is  found  thus  : 

The  pump  was  so  carefuOy  made,  that  no  water 
escaped  back  through  the  leathers,  it  dehvered  the  same 
quantity  each  stroke,  whether  quick  or  slow,  and  by 
ascertaininf^  the  quantity  of  12  strokes  and  counting  the 
number  of  strokes  in  a  minute,  that  was  sufficient  to 
keep  the  surface  of  the  water  to  the  same  height,  the 
quantity  expended  was  found. 

These  things  will  be  further  illustrated  by  going  over 
the  calculations  of  one  set  of  experiments. 

Specimen  of  a  set  of  experiments. 

The  sluice  drawn  to  the  1st  hole. 
The  water  above  the  floor  of  the  sluice     30  inch. 
Strokes  of  the  pump  in  a  minute,  39| 

The  head  raised  by  12  strokes,  21  inch. 

The  wheel  raised  the  empty  scale  and 

made  turns  in  a  minute. 
With  a  c'ouiTter-weisrht  of  1  lb.  8  oz.  it  7  „- 

made  5 

Ditto,  tried  with  water,  86 

No.  lbs.  oz.        tumsinamin.      product, 

1  4:0  45  180 

2  5:0  42  210 

3  6:0  36|  2ir| 

4  7:0  33|  236| 

5  8:0  30  240  max. 

6  9:0  26i  238| 
r  10  :  0  22  220 

8  11:0         16i        181| 

9  12  :  O  *  ceased  working. 

Counter- weight  for  30  turns  without  water  2  oz.  in 
the  scale. 

N.  B.  The  area  of  the  head  was  105,8  square  inches, 
weight  of  the  empty  scale  and  pulley  10  ounces,  circum- 

*  When  the  wheel  moves  so  slow  as  not  to  rid  the  water  so  fast  as  sap- 
plied   by  the  sluice,  the  accumulated  water  falls  back  upon  the  aperture, 
and  the  wheel  immediately  ceases  moving- 
Note.  This  note  of  the  author  argues  in  favour  of  drawing  the  gate  near 
the  60.115. 


Chap.  12.]  HYDRAULICS.  "  127 

ference  of  the  cylinder  9  inches,  and  circumference  of 
the  water-wheel  75  inches. 

Reduction  of  the  above  Set  of  Experiments. 

The  circumference  of  the  wheel  75  inches,  multiplied 
by  86  tons,  gives  6450  inches  for  the  velocity  of  the 
water  in  a  minute,  1-60  of  which  will  be  the  velocity  in 
a  second,  equal  to  107,5  inches,  or  8,96  feet,  which  is 
due  to  a  head  of  15  inches,*  and  this  we  call  the  virtual 
or  effective  head. 

The  area  of  the  head  being  105,8  inches,  this  multi- 
plied by  the  weight  of  water  of  one  cubic  inch,  is  equal 
to  the  decimal  of  ,579  of  the  ounce  avoirdupois,  gives 
61,26  ounces  for  the  weight  of  as  much  water  as  is  con- 
tained in  the  head  upon  one  inch  in  depth,  1-10  of  which 
is  3,831b.  this  multiplied  by  the  depth  21  inches  gives 
80,431b.  for  the  value  of  IS  strokes,  and  by  proportion 
39|  (the  number  made  in  a  minute)  will  give  264,71b- 
the  weight  of  water  expended  in  a  minute. 

Now  as  364,71b.  of  water  may  be  considered  as  hav- 
ing descended  through  a  space  of  15  inches  in  a  minute,, 
the  product  of  these  two  numbers  3970  will  express  the 
power  of  the  water  to  produce  mechanical  effects  ;  which 
are  as  follows. 

The  velocity  of  the  wheel  at  a  maximum  as  appears 
above,  was  30  turns  in  a  minute ;  which  multiplied  by 
9  inches,  the  circumference  of  the  cylinder,  makes  270 
inches  :  but  as  the  scale  was  hung  by  a  pulley  and  dou- 
ble line,  the  weight  was  only  raised  half  of  this,  viz. 
135  inches. 

The  weia;ht  in  the  scale  at  the  7  on         r. 

•  *=*  S-  81b.       0  oz. 

maximum.  ^ 

Weight  of  the  scale  and  pul-  ^  ^i,       ,^ 
ley,  ^       .  oz. 

Counter- weidit,     scale,    and7/->iu      in 
pulley,      ^  ^^^^-     12  oz. 

Sum  of  the  resistance,  91b.     6  oz.   or  9,375Ib. 

*  This  is  determined  by  the  common  maxim  of  hydrostatics;  that  the 
velocity  of  spoutincj  water  is  equal  to  the  velocity  that  a  heavy  body  would 
require  in  fallinu  from  the  height  of  the  reservoir;  and  is  proved  by  tbf 
rising  of  .iets,  to  the  height  of  tJieir  reservoirs  nearly. 


128  HYDRAULICS.  [Chap.  12. 

Now,  as  9,3751b  is  raised  135  inches,  these  two  num- 
bers being  multiphed  together  produces  1266,  which 
expresses  the  effect  produced  at  a  maximum  :  so  that 
the  proportion  of  the  power  to  the  effect  is  as  3970 :  1266, 
or  as  10:3,18. 

But  though  this  is  the  greatest  single  effect  producible 
from  the  power  mentioned,  by  the  impulse  of  the  water 
upon  an  undershot  wheel ;  yet  as  the  whole  power  of  the 
water  is  not  exhausted  thereby,  this  will  not  be  the  true 
ratio  between  the  power  and  the  sum  of  all  the  effects 
producible  therefrom  :  for  as  the  water  must  necessarily 
leave  the  wheel  with  a  velocity  equal  to  the  circum- 
ference, it  is  plain  that  some  part  of  the  power  of  the 
water  must  remain  after  leaving  the  wheel. 

The  velocity  of  the  wheel  at  a  maximum  is  30  turns 
a  minute,  and  consequently  its  circumference  moves  at 
the  rate  of  3,123  feet  per  second,  which  answers  to  a 
head  of  1,82  inches:  this  being  multiplied  by  the  ex- 
pense of  water  in  a  minute,  viz.  264i,71b.  produces  481 
for  the  power  remaining,  this  being  deducted  from  the 
original  power  3970,  leaves  34)89  which  is  that  part  of 
the  power  that  is  spent  in  producing  the  effect  1266,  so 
that  the  power  spent  34h9  is  to  its  greatest  effect  1266, 
as  10:3,62,  or  as  ll  :4'. 

The  velocity  of  the  water  striking  the  wheel  86  turns 
in  a  minute,  is  to  the  velocity  at  a  maximum  30  turns  a 
minute,  as  10 : 3,5  or  as  20  to  7,  so  that  the  velocity  of 
the  wheel  is  a  little  more  than  1-3  of  the  velocity  of  the 
water. 

The  load  at  a  maximum  has  been  shewn  to  be  equal 
to  91b.  6oz.  and  that  the  wheel  ceased  moving  with  121b. 
in  the  scale  :  to  which  if  the  weight  of  the  scale  be  added, 
viz.  10  oz.*  the  proportion  will  be  nearly  as  3  to  ■*,  be- 
tween the  load  at  a  maximum  and  that  by  which  the 
wheel  is  stopped.f 

*  The  resistance  of  the  air  in  this  case  ceases,  and  the  friction  is  not 
added,  as  12  lb.  in  the  scale  was  sufficient  to  stop  the  wheel  after  it  had 
been  in  full  motion,  and  therefore  somewhat  more  than  a  counter-balance 
for  the  impulse  of  the  water. 

f  I  may  here  observe,  that  it  is  probable,  that  if  the  g'ate  of  the  sluice 
had  been  drawn  as  near  the  float-boards  as  possible,  (as  is  the  practice  in 
America,  where  water  is  applied  to  act  by  impulse  alone,)  that  the  wheel 


Chap.  12.]  HYDRAULICS.  129 

It  is  somewhat  remarkable,  that  though  the  velocity 
of  the  wheel  in  relation  to  the  water  turns  out  greater 
than  1-3  of  the  velocity  of  the  water,  yet  the  impulse  of 
the  water  in  case  of  the  maximum  is  more  than  double 
of  what  is  assigned  by  theory  ;  that  is,  instead  of -i-Q  of 
the  column,  it  is  nearly  equal  to  the  whole  column.* 

It  must  be  remembered,  therefore,  that  in  the  present 
case,  the  wheel  was  not  placed  in  an  open  river  where 
the  natural  current,  after  it  has  communicated  its  impulse 
to  the  float,  has  room  on  all  sides  to  escape,  as  the 
theory  supposes  ;  but  in  a  conduit  or  race,  to  which  the 
float  being  adapted,  the  water  cannot  otherwise  escape 
tlian  by  moving  along  with  the  wheel.  It  is  observable, 
that  a  wheel  working  in  this  njanner,  as  soon  as  the  water 
meets  the  float,  it  receiving  a  sudden  check,  rises  up 
against  the  float,  like  a  wave  against  a  fixed  object,  in- 
somuch, that  when  the  sheet  of  water  is  not  a  quarter  of 
an  inch  thick  before  it  meets  the  float,  yet  this  sheet 
will  act  upon  the  whole  surface  of  a  float,  whose  height 
is  three  inches ;  consequendy,  was  the  float  no  higher 
than  the  thickness  of  the  sheet  of  water,  as  the  theory 
also  supposes,  a  great  part  of  the  force  ^vouId  be  lost  by 
the  water  dashing  over  the  float. 

In  confirmation  of  what  is  already  delivered,  I  have 
adjoined  the  following  table,  containing  the  result  of  27 
experiments  made  and  reduced  in  the  manner  above 
specified.  What  remains  of  the  theory  of  undershot 
wheels,  will  naturally  follow  from  a  comparison  of  the 
different  experiments  together. 

would  have  continued  to  move  until  loaded  with  I  1-2  times  the  weight  of 
the  maximum  load,  viz.  9lb.  6  oz.  multiplied  by  1  1.2,  is  equal  to  141b.  1  oz. 
Then  it  would  have  agreed  with  the  theory  established  art.  41.  This  pier- 
haps  escaped  the  notice  of  our  author. 

•  This  observation  of  the  author  t  think  a  strong  confirmation  of  the 
truths  of  the  theory  established  art.  41 ;  where  the  maximum  velocity  is 
made  to  be  ,577  parts  of  the  velocity  of  the  water,  and  the  load  to  be  2-3 
the  greatest  load  :  For  if  the  gate  had  been  drawn  near  the  floats,  the 
greatest  load  would  probably  have  been  I41b.  1  oz.  ocas  ?  to  2,  of  thft 
maximum  load. 


130 


HYDRAULICS. 


[Chap.  1^ 


A  TABLE  OF  EXPERIMENTS, 

No.  I. 


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lbs. 

1 

33 

88 

15,85 

30 

13  10 

10     9 

275 

4358 

1411 

10:3,24 

10:3,4 

10:7,75 

2 

30 

86 

15, 

30 

12  10 

9     6 

264,7 

3970 

1266 

10:3,2 

10:3,5 

10:7,4 

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3 

27 

82 

13,7 

28 

11     2 

8     6 

243 

3329 

1044 

10:3,15 

10:3,4 

10:7.5 

4 

24 

78 

12,3 

27.7 

9  10 

7     5 

235 

2890 

901.4 

10:3,12 

10:3,55 

10:7,53 

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5 

21 

75 

11,4 

25,9 

8  10 

6     5 

214 

2439 

735,7 

10:302 

10:3,45 

10:7,32 

6 

18 

70 

9,95 

23,5 

6  10 

5     5 

199 

1970 

561,8 

10:2,85 

10:3,36 

10:8,02 

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15 

65 

8,54 

23,4 

5     2 

4    4 

178,5 

1524 

442,5 

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10:3  6 

10:8,3 

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60 

7,29 

22 

3  10 

3     5 

161 

1173 

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5,47 

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134 

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114 

404,7 

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2993 

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9,6 

25 

7  10 

6  14 

277 

2659 

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385 

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13 

Chap.  12.]  HYDRAULICS.  13i 


Maxims  and  Observations  deduced  from  the  foregoing 
Table  of  Experiments. 

Max.  1.  That  the  virtual  or  effective  head  being  the 
same,  the  effect  will  be  nearly  as  the  quantity  of  water 
expended. 

This  will  appear  by  comparing  the  contents  of  the 
columns  4,  8  and  10,  in  the  foregoing  sets  of  experi- 
ments, as  for 

Example  I.  taken  from  No  8  and  S5,  viz. 

No.  Virtual  head.  Water  expended.  Effect, 

8  7,29  161  328 

25  7,29  355  785 

Now  the  heads  being  equal,  if  the  effects  are  propor- 
tioned to  the  water  expended,  we  shall  have  by  maxim 
I.  as  161 :  356 ::  328 :  723 ;  but  723  falls  short  of  785,  as  it 
turns  out  in  experiment,  according  to  No.  25  by  62. 
The  effect  therefore  of  No.  25,  compared  with  No  8,  is 
greater  than,  according  to  the  present  maxim,  in  the  ratio 
of  14  to  13.* 

The  foregoing  example  with  four  similar  ones  are  seen 
at  one  view  in  the  foregoing  table. 

•  If  the  true  maximum  velocity  of  the  wheel  be  ^Sn  of  the  Telocity  of 
the  water,  and  (he  true  maximum  load  be  2-3  of  the  whole  column,  as 
shewn  in  art.  42 ;  then  the  effect  will  bethe  power  in  the  ratio  of  100  to 
38,  or  as  10  to  3,8,  a  little  more  than  appears  by  the  table  of  experiments, 
in  columns  9  and  10  :  the  difference  is  owing  to  the  disadyantageous  appli- 
cation of  the  water  on  the  wheel  in  the  model. 


132 


HYDRAULICS. 


[Ghap.  12. 


A  TABLE  OF  EXPERIMENTS, 

No.  II. 


Proportional 
variation. 

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No.  Table  I. 
Examples. 

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to  1^ 

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in 

Chap.  12.]  HYDRAULICS.  133 

By  this  table  of  experiments  it  appears  that  some  fall 
short  and  others  exceed  the  maximum,  and  all  agree  as 
near  as  can  be  expected  in  an  affair  w  here  so  many  dif- 
ferent circumstances  are  concerned ;  therefore  we  may 
conclude  the  maxim  to  be  true. 

Max.  II.  That  the  expense  of  the  water  being  the 
same,  the  effect  will  be  nearly  as  the  height  of  the  vir- 
tual or  effective  head. 

This  also  will  appear  by  comparing  the  contents  of 
columns  4,  8  and  10,  in  any  of  the  sets  of  e;5cperimentS; 

Example  I.  of  No.  2  and  No.  24. 

No.  Virtual  head.  Expense-  Effect. 

S  15  264,7  1266 

24  4,7  262  385 

Now  as  the  expenses  are  not  quite  equal,  we  must 
proportion  one  of  the  effects  accordingly,  thus  : 
By  maxim  I.         292:26-1,7::  385:389 
And  by  max.  II.     15 :     4,7 : :  1266 :  397 

Difference,       8 

The  effect  therefore  of  No.  24,  compared  with  No.  2, 
is  less  than,  according  to  the  present  maxim,  in  the  ratio 
of  49  :  50. 

Max.  III.  That  the  quantity  of  water  expended  being 
the  same,  the  effect  is  nearly  as  the  square  root  of  its 
velocity. 

This  will  appear  by  comparing  the  contents  of  co- 
lumns 3,  8  and  10,  in  any  set  of  experiments  ;  as  for 

Example  I.  of  No.  2  xvith  No.  24,  viz. 

No.        Turns  in  a  minute-  Expense.  Effect. 

2  86  264,7  1266 

24  48  262,  385 

The  velocity  being  as  the  number  of  turns,  we  shall 
have 


134.  HYDRAULICS.  [Chap.  i2. 

By  maxim  I.  2Q2 :  264,7         ::  385 :  389 

And  by  max.  III.      >      4^«       *^  f::  1266: 394 

•'  /       /39b:  230*  S 


Difference,     5 

The  effect  of  No.  24,  compared  with  No.  2,  is  less 
than  by  the  present  maxim  in  the  ratio  of  78  :  79. 

Max.  IV.  The  aperture  being  the  same,  the  effect 
will  be  nearly  as  the  cube  of  the  velocity  of  the  water. 

This  also  will  appear  by  comparing  the  contents  of 
colmnns  3,  8  and  10,  as  for 

Example  of  J\'o.  1,    mid  JVb.  10,  viz. 

No.  Turns.  Expense.  EfFect. 

1  88  275  1411 

10  42  114  117 

Lemma.  It  must  here  be  observed,  that,  if  water 
passes  out  of  an  aperture  in  the  same  section,  but  with 
different  velocities,  the  expense  will  be  proportional  to 
the  velocity  ;  and  therefore  conversely,  if  the  expense 
is  not  proportional  to  the  velocity,  the  section  of  water  is 
not  the  same. 

Now  comparing  the  water  discharged  with  the  turns 
of  No.  1  and  10,  \Ve  shall  have  88  :  42 ::  275  :  131,2  ;  but 
the  water  discharged  by  No.  10  is  only  1141b.  therefore, 
though  the  sluce  was  drawn  to  the  same  height  in  No. 

10  as  in  No.  1  :  yet  the  section  of  the  water  passing  out, 
was  less  in  No.  10  than  No  1,  in  the  proportion  of  114 
to  131,2,  consequently  had  the  effective  aperture  or  sec- 
tion of  the  water  been  the  same  in  No.  10  as  in  No  1,  so 
that  131,21b.  of  water  h*d  been  discharged,  instead  of 

11  lib.  the  effect  would  have  been  increased  in  the  same 
proportion  :  that  is. 

By  lemma  88:  42         ::  275:131,2 

Bv  maxim  I.  114  :        1312     ::  117:134,5 


And  by  max.  IV.  j  681472  •  ''^"""  ^  '^'^^^  '  *^^'^ 


Difference     19 


Chap.  12.]  HYDRAULICS.  135 

The  effect  therefore  of  No.  10,  compared  with  No.  1, 
is  less  than  ought  to  be,  by  the  present  maxim,  in  the 
ratio  of  y:8. 

OBSERVATIONS. 

Observ.  1st.  On  comparing  columns  2  and  4,  table  I. 
it  is  evident,  that  the  virtual  head  bears  no  certain  pro- 
portion to  the  head  of  water,  but  that  when  the  aperture 
is  greater,  or  the  velocity  of  the  water  issuing  therefrom 
less,  they  approach  nearer  to  a  coincidence  :  and  conse- 
quently in  the  large  opening  of  mills  and  sluices,  where 
great  quantities  of  water  are  discharged  from  moderate 
heads,  the  head  of  water  and  virtual  head  determined 
from  the  velocity  will  nearer  agree,  as  experience  con- 
firms. 

Observ.  2nd.  Upon  comparing  the  several  proportions 
between  the  powers  and  effects  in  column  11th,  the  most 
general  is  that  of  10  to  3;  the  extremes  are  10  to  3,2  and 
10  to  2,8;  but  as  it  is  observable,  that  where  the  quantity 
of  water  or  the  velocity  thereof  is  great,  that  is,  where  the 
power  is  greatest,  the  2nd  term  of  the  ratio  is  greatest 
also,  we  may  therefore  well  allow  the  proportion  subsist- 
ing in  large  works  as  3  to  1 . 

Observ.  Srd.  The  proportion  of  velocities  between 
the  water  and  wheel  in  column  12  are  contained  in  the 
limits  of  3  to  1  and  2  to  1;  but  as  the  greater  velocities 
approach  the  limits  of  3  to  1,  and  the  greater  quantity  of 
water  approach  to  that  of  2  to  1,  the  best  general  propor- 
tion will  be  that  of  5  to  2.* 

Observ.  4th.  On  comparing  the  numbers  in  column 
13,  it  appears,  that  there  is  no  certain  ratio  between  the 

•  I  may  here  observe,  that  our  friend  Smeaton  may  be  wrong'  in  his  con- 
clusion, that  the  best  general  ratio  of  the  velocity  of  the  water  to  that  of 
the  wheel  will  be  as  5  to  2 ;  because,  we  may  observe,  that  in  the  first  ex- 
periment, where  the  virtual  head  was  15,85  inches,  and  the  gate  drawn  to 
the  1st  hole,  the  ratio  is  as  10  :  3,4.  But  in  the  last  experiment,  where 
the  head  was  5,03  inches,  and  gate  drawn  to  the  6th  hole,  the  ratio  is  as 
10  :  5,2;  and  that  the  2nd  term  of  the  ratio  increases  gradually,  as  the  head 
decreases,  and  quantity  of  water  increases ;  therefore  we  may  conclude, 
that  in  the  large  openings  of  mills,  that  the  ratio  may  approach  to  3  to  2  ; 
which  will  agree  with  the  practice  and  experiments  <  f  many  able  mill- 
wrights, of  America,  and  many  experiments  1  have  made  on  mills.  And  as 
it  is  better  to  give  the  wheel  a  velocity  too  great  than  too  slow,  I  conclude, 
the  wheel  of  an  imdershot  mill  must  have  nearly  2-3d  of  the  velocity  of  the 
water  to  produce  a  jnaximum  effect. 


136  HYDRAULICS.  [Chap.  12. 

load  that  the  wheel  will  carry  at  its  maximum,  and  what 
will  totally  stop  it ;  but  that  they  are  contained  within 
the  limits  of  20  to  19  and  of  20  to  15  ;  but  as  the  effect 
approaches  nearest  to  the  ratio  of  20  to  15  or  of  4  to  3, 
when  the  power  is  greatest,  whether  by  increase  of  velo- 
city or  quantity  of  water,  this  seems  to  be  the  most 
applicable  to  large  works  :  but  as  the  load  that  a  wheel 
ought  to  have  in  order  to  work  to  the  best  advantage,  can 
be  assigned  by  knowing  the  effect  it  ought  to  produce,- 
and  the  velocity  it  ought  to  have  in  producing  it,  the 
exact  knowledge  of  the  greatest  load  that  it  will  bear  is 
of  less  consequence  in  practice.* 

It  is  to  be  noted,  that  in  almost  all  of  the  examples 
under  the  three  last  maxims  (of  the  four  preceding)  the 
effect  of  the  lesser  power  falls  short  of  its  due  propor- 
tion to  the  greater,  when  compared  by  its  maxim.  And 
hence,  if  the  experiments  are  taken  strictly,  we  must 
infer  that  the  effects  increase  and  diminish  in  an  higher 
ratio  than  those  maxims  suppose  ;  but  as  the  deviations 
are  not  very  considerable,  the  greatest  being  about  1-8 
of  the  quantity  in  question,  and  as  it  is  not  easy  to  make 
experiments  of  so  compound  a  nature  with  absolute 
precision,  we  may  rather  suppose  that  the  lesser  power 
is  attended  with  some  friction,  or  works  under  some 
disadvantage,  not  accounted  for  :  and  therefore  we  may 
conclude,  that  these  maxims  will  hold  very  nearly, 
vv'hen  applied  to  works  in  large. 

After  the  experiments  above-mentioned  were  tried, 
the  wheel  which  had  24  floats  was  reduced  to  12,  which 
caused  a  diminution  in  the  effect  on  account  of  a  greater 
quantity  of  water  ei^caping  between  the  floats  and  the 
floor,  but  a  circular  sweep  being  adapted  thereto,  of  such 
a  length  that  one  float  entered  the  curve  before  the  pre- 
ceding one  quitted  it,  the  effect  came  so  near  to  the 
former,  as  not  to  give  hopes  of  increasing  the  effect  by 
increasing  the  number  of  floats  past  24,  in  this  particular 
wheel. 

*  Perhaps  the  author  is  here  again  deceived  by  the  imperfection  of  the 
model ;  for  had  the  water  been  drawn  close  to  the  float,  the  load  that 
would  totally  stop  the  wheel  would  always  be  equal  to  the  column  of  water 
acting  on  the  wheel.  See  the  note  page  70.  The  friction  of  the  shute  and 
air  destroyed  great  part  of  the  force  of  his  small  quantity  of  water. 


Chap.  12.]  HYDRAULICS.  13^ 

ART.    68. 

PART  II. 

CONCERNING  OVERSHOT  WHEELS. 

In  the  former  part  of  this  essay,  we  have  considered 
the  impulse  of  a  confined  stream,  acting  on  undershot 
wheels;  we  now  proceed  to  examine  the  power  and 
application  of  water,  when  acting  by  its  gravity  on  over- 
shot wheels. 

It  will  appear  in  the  course  of  the  following  deduc- 
tions, that  the  effect  of  the  gravity  of  descending  bodies, 
is  very  different  from  the  effect  of  the  stroke  of  such  as 
are  non-elastic,  though  generated  by  an  equal  mechanical 
power. 

The  alterations  of  the  machinery  already  described, 
to  accommodate  the  same  for  experiments  on  overshot 
wheels,  were  principally  as  follow. 

Plate  XII.  The  sluice  I  b  being  shut  down,  the  rod 
H  I  was  taken  off.  The  undershot  water-wheel  was 
taken  off  the  axis,  and  instead  thereof,  an  overshot 
wheel  of  the  same  size  and  diameter  was  put  in  its  place. 
Note,  this  wheel  was  2  inches  deep  in  the  shroud  or 
depth  of  the  bucket,  the  number  of  buckets  was  36. 

A  trunk  for  bringing  the  water  upon  the  wheel  was 
fixed  according  to  the  dotted  lines  f  g,  the  aperture  was 
adjusted  by  a  shuttle  which  also  closed  up  the  outer  end 
of  the  trunk,  when  the  water  was  to  be  stopped. 


i3  8  HYDRAULICS.  [Chap.  12. 


Specimen  of  a  Set  of  Experime?ifs. 

Head  6  inches — 14|  strokes  of  the  pump  in  a  minute, 
12  ditto=801b.*  weight  of  the  scale  (being  wet)  10| 
ounces. 

Counter-weight  for  20  turns  besides  the  scale,  3  ounces. 


No. 

wt.  in  the  scale. 

turns. 

product. 

observations. 

1 

0 

60 

)  threw  most  part  of 

2 

1 

56 

i 

i 

>  the   \\'ater    out    of 

3 

2 

iiS 

\ 

\  the  wheel. 

/  received  the  water 

4i 

3 

49 

147  ; 

5 

4 

47 

188    ' 

\  more  quietly. 

6 

5 

45 

335 

7 

6 

43i 

355 

8 

7 

41 

387 

9 

8 

381 

808 

10 

9 

36i 

3381 

11 

10 

35| 

355 

13 

11 

33| 

360| 

13 

13 

31i 

375 

14. 

13 

38  i 

370| 

15 

14 

S7| 

385 

16 

15 

36 

390 

17 

16 

34i 

393 

18 

17 

331 

386| 

19 

18 

31| 

391 1 

20 

19 

S0| 

394|;. 

> 

2i 

20 

19| 

395    < 

>  maximum. 

22 

31 

18i 

383| " 

S3 

S3 

18 

396  worked  irre.8:ular. 

34 

33 

overset 

by  its  loa 

d. 

*  The  small  difierence  in  the  value  of  12  strokes  of  the  pump  from  the 
former  experiments,  was  owing  to  a  small  diflf'erence  in  the  length  of  the 
stroke,  occasioned  by  the  warping  of  the  wood. 


Chap.  12.]  HYDRAULICS.  139 

Reduction  of  the  preceding  Specimen. 

In  these  experiments  the  head  being  6  inches,  and  the 
heip;ht  of  the  wheel  24  inches,  the  whole  descent  will 
be  30  inches  :  the  expense  of  watei'  was  14^  strokes  of 
the  pump  in  a  minute,  whereof  12  contained  80lb.  there- 
fore the  water  expended  in  a  minute,  was  96  S-31b. 
which  multiplied  by  30  inches,  gives  the  power=2900. 

If  we  take  the  SOth  experiment  for  the  maximum,  we 
shall  have  20|  turns  in  a  minute,  each  of  which  raised 
the  weight  4|  inches,  that  is,  93.37  inches  in  a  minute. 
The  weight  in  the  scale  was  19!bs.  the  weight  of  the 
scale  lOi  oz.  the  counter-weight  3  oz.  in  the  scale,  which, 
with  the  weight  of  the  scale  10 1  oz.  makes  in  the  whole 
20|lb.  which  is  the  whole  resistance  or  load,  this  multi- 
plied by  93,37,  makes  1W14  for  the  effect. 

The  ratio  therefore  of  the  power  and  effect  will  be  as 
S900:191*,  or  as  10:6,6,  or  as  3  to  2  nearly. 

But  if  we  compute  the  power  from  the  height  of  the 
wheel  only,  we  have  96  2-31b.  xS4<  inches=:S820  for  the 
power,  and  this  will  be  to  the  effect  as  2320:1914  or  as 
10:8,2,  or  as  5  to  4  nearly. 

The  reduction  of  this  specimen  is  set  down  in  No.  9 
of  the  following  table,  and  the  rest  were  deducted  from 
a  similar  set  of  experiments,  deduced  in  the  same  manner. 


140 


HYDRAULICS. 


[Ghap.  12; 


TABLE  III. 


CONTAINING  THE  RESULT  OF  16  SETS  OF  EXPERIMENTS  ON 
OVERSHOT  WHEELS. 


— 

P3         1 

7i 

H 

»= 

p 

^ 

T 

^ 

T3 

O 

o 

p 

2. 

o 

o 

o 

crq 

■*> 

cr 

re 

-0 

^* 

'  ' 

-t 

3" 

^ 

n 

o 

P 

o 

re 

re 

3 

re 

B 
3" 

2. 

in' 

re 

re 

-5 
C 

o 

•a 

o 

re   ^ 

a  re 

re 

3 

cr 

<r 

C- 

=r 

=r 

o 

-o 

So 

S 

-1 

-3 

3 

p 

o 

-• 

(D 

o 

re 

P 

^ 

f— 

o 

"» 

3 

re 

-* 

» 

p. 

-i 

3 

■■3 

X 

UI 

rt 

» 

^ 

3 

3 

3 

re 

C- 

3- 

rt 

3 
C 

3 

3 

re 

iv 
o 

re 

M 
3 

— 

lbs. 

c- 

UK  hs 

I  b 

1 

27 

30 

19 

6  1-2 

810 

720 

0556 

10   :    6,9 

10    :   7,7 

2 

27 

56  2-3 

16  1-4 

14  1-2 

1530 

1360 

1060 

10   :    6,9 

10  :  7,8 

^'^ 

3 

97 

56  2  3 

20  3  4 

12  12 

1530 

1360 

1167 

10  :  7,6 

10  :  8,4 

..   c. 

4 

27 

63  1-3 

20  12 

13  1-2 

1710 

1524 

1245 

10  :   7,3 

10  :  8.2 

CO  c 

5 
6 

27 

762-3 

21  12 
18  3-4 

15  1-2 

2070 

1840 
1764 

1500 
1476 

10   :   7,3 

10  :  8,2 

2812 

73  1-3 

17  1-2 

2090 

10  :  7 

10  :  8,4 

~>  c 

7 
8 

281  2 
30 

96  2-3 

20  14 
20 

20  1  2 
19  1  2 

2755 
2700 

2320 
2160 

1868 
1755 

10  :  6,8 

10  :  8,1 

to  ■• 

o 

90 

10  :  65 

10  :   8,1 

9 

30 

96  2  3 

20  3-4 

20  1-2 

2900 

2320 

1914 

10   :  6,6 

10   :    8,2 

10 
11 

30 

113  13 

21 

20  1-4 

23  1-2 

3400 

2720 
1360 

2221 
1230 

10  :  6,5 

10    :    8,2 

"k; 

33 

56  2-3 

13  1-2 

1870 

10  :  6,6 

10    :  8 

>-* 
o 

12 

33 

106  23 

22  1-4 

21  1-2 

352u 

2560 

2153 

10  :  6,1 

10    :      '4 

13 
14 

33 

146  2-3 

23 

19  3  4 

27  12 

4840 

3520 

2846 

10  :  5,9 

10  :  8.ih- 

35 

65 

16  12 

2275 

15601466 

10  :  6.5 

10   :  9,4 

o 

15 

35 

120 

21  1-2 

25  1-2 

4200 

2880  2467 

10  :   5,9 

10  :  8,6 

16 

1 

35 

163  1  2 

25 
4 

26  1-2 
5 

:5728 
i    6 

39242981 

10   :   5,_ 

10  :  7.6 

Ot 

2 

i      3 

7 

8 

9 

1    10 

11 

Chap.  12.]  HYDRAULICS.  141 


OBSERVATIONS   AND   DEDUCTIONS  FROM   THE    FOREGOING 
EXPLRIMENTS 

I.   Concerning  the  Ratio  between  the  Power  and  Effect 
of  Overshot  JVheels. 

The  effective  power  of  the  water  must  be  reckoned 
upon  the  whole  descent,  because  it  must  be  raised  to  that 
height  in  order  to  be  in  a  condition  of  producing  the  same 
effect  a  second  time. 

The  ratios  between  the  powers  so  estimated,  and  the 
effects  at  a  maximum  deduced  from  the  several  sets  of 
experiments,  are  exhibited  at  one  view  in  column  9  of 
table  III ;  and  hence  it  appears,  that  those  ratios  differ 
from  that  of  10  to  7,6  to  that  of  10  to  5,S;  that  is,  nearly 
from  4  to  3  to  4:2.  In  those  experiments,  where  the 
heads  of  water  and  quantities  expended  are  least,  the 
proportion  is  nearly  as  4  to  3;  but  where  the  heads  and 
quantities  are  greatest,  it  approaches  nearer  to  that  of 
4  to  2,  and  by  a  medium  of  the  whole  the  ratio  is  that  of 
3:2  nearly.  We  have  seen  before  in  our  observations 
upon  the  effects  of  undershot  wheels,  that  the  general 
ratio  of  the  power  to  the  effect,  when  greatest,  was  as 
3:1.  The  effect,  therefore,  of  overshot  wheels,  under  the 
same  circumstances  of  quantity  and  fall,  is  at  a  medium 
double  to  that  of  the  undershot :  and  a  consequence 
thereof,  that  non-elastic  bodies  when  acting  by  their  im- 
pulse or  collision,  communicate  only  a  part  of  their  ori- 
ginal power  :  the  other  part  being  spent  in  changing 
their  figure  in  consequence  of  the  stroke.* 

The  powers  of  v\  ater  computed  from  the  height  of  th^ 
wheel  only,  compared  with  the  effects  as  in  column  10, 
appear  to  observe  a  more  constant  ratio  :  for  if  we  take 
the  medium  of  each  class,  which  is  set  down  in  column 
11,  we  shall  find  the  extreme  to  differ  no  more  than 
from  the  ratio  of  10:8,1  to  that  of  10:8,5,  and  as  the 
second  term  of  the  ratio  gradually  increases  from  8,1  to 
8,5  by  an  increase  of  head  from  3  inches  to  11,  the  ex- 

•  These  observations  of  the  author  agree  with  the  theory,  art.  41 — 42. 
I  may  add,  thai  non-elas.lc  bodies,  when  acting  by  impulse  or  collision, 
communicate  only  half  of  their  original  power,  by  the  laws  of  motion. 


143  HYDRAULICS.  [Chap.  12. 

cess  of  8,5  above  8,1  is  to  be  imputed  to  the  superior 
impulse  of  the  water,  at  the  head  of  11  inches  above  that 
of  3  inches,  so  that  if  we  reduce  8,1  to  8,  on  account  of 
the  impulse  of  the  3  inch  head,  we  shall  have  the- ratio  of 
the  power  computed  upon  the  height  of  the  wheel  only, 
to  the  effect  at  a  maximum,  as  10:8  or  as  5:4  nearly. 
And  from  the  equality  of  the  ratio,  between  power 
and  effect,  subsisting  where  the  constructions  are  similar, 
we  must  infer  that  the  effects  as  well  as  the  powers,  are 
as  the  quantities  of  water  and  perpendicular  heights,  mul- 
tiplied together  respectively. 

II.   Concerning  the  most  proper-  Height  of  the  Wheel  in 
Proportion  to  the  whole  descent. 

We  have  already  seen  in  the  preceding  observation, 
that  the  effect  of  the  same  quantity  of  water,  descending 
through  the  same  perpendicular  space,  is  double,  when 
acting  by  its  gravity  upon  an  overshot  wheel,  to  what 
the  same  produces  when  acting  by  its  impulse,  upon  an 
undershot.  It  also  appears,  that  by  increasing  the  head 
from  3  to  11  inches,  that  is,  the  whole  descent,  from  S7 
to  35,  or  in  the  ratio  of  7  to  9  nearly,  the  effect  is  ad- 
vanced no  more  than  in  the  ratio  of  8,1  to  8,4 ;  that  is, 
as  7:7,^6,  and  consequently  the  increase  of  the  effect  is 
not  1-7  of  the  increase  of  the  perpendicular  height. 
Hence,  it  follows,  that  the  higher  the  wheel  is  in  propor- 
tion to  the  whole  descent,  the  greater  will  be  the  effect ; 
because  it  depends  less  upon  the  impulse  of  the  head, 
and  more  upon  the  gravity  of  the  water  in  the  buckets  : 
and  if  we  consider  how  obliquely  the  water  issuing  from 
the  head  must  strike  the  buckets,  we  shall  not  be  at  a 
loss  to  account  for  the  httle  advantage  that  arises  from 
the  impulse  thereof;  and  shall  immediately  see  of  how 
htde  consequence  this  impulse  is  to  the  effect  of  an 
overshot  wheel.  However,  as  every  thing  has  its  limits, 
so  has  this :  for  thus  much  is  desirable,  that  the  water 
should  have  somewhat  greater  velocity,  than  the  circum- 
ference of  the  wheel,  in  coming  thereon  :  otherwise  the 
wheel  will  not  only  be  retarded  by  the  buckets  striking 
the  water,  but  thereby  dashing  a  part  of  it  over:  so  much 
of  the  power  is  lost. 


Ghap.12.]  HYDRAULICS.  143 

The  velocity  that  the  circumference  of  the  wheel 
ought  to  have  being  known,  the  head  requisite  to  give 
the  water  its  proper  velocity  is  easily  found,  by  the  com- 
mon rules  of  hydrostatics,  and  will  be  found  much  less 
than  what  is  commonly  practised. 

III.   Concei'ning  the  Velocity  of  the  circumference  of  the 
Wheel  in  order  to  produce  the  greatest  effect. 

If  a  body  is  let  fall  freely  from  the  surface  of  the  head 
to  the  bottom  of  the  descent,  it  will  take  a  certain  time 
in  falling ;  and  in  this  case  the  whole  action  of  gravity  is 
spent  in  giving  the  body  a  certain  velocity  :  But,  if  this 
body  in  falling  is  made  to  act  upon  some  other  body,  so 
as  to  prcjduce  a  mechanical  effect,  the  falling  body  will 
be  retarded ;  because,  a  part  of  the  action  of  gi'avity  is 
then  spent  in  producing  the  effect,  and  the  remainder 
only  giving  motion  to  the  falling  body  :  and,  therefore, 
the  slower  a  body  descends,  the  greater  will  be  the  por- 
tion of  the  action  of  gravity  applicable  to  the  producing 
a  mechanical  effect.  Hence  we  are  led  to  this  general 
rule,  that  the  less  the  velocity  of  the  wheel,  the  greater 
will  be  the  effect  thereof.  A  confirmation  of  this  doc- 
ti'ine,  together  with  the  limits  it  is  subject  to  in  practice, 
may  be  deduced  from  the  foregoing  specimen  of  a  set 
of  experiments. 

From  these  experiments  it  appears,  that  when  the 
wheel  made  about  20  turns  in  a  minute,  the  effect  was 
nearly  upon  the  greatest ;  when  it  njade  30  turns,  the 
effect  was  diminished  about  1-20  part ;  but,  that  when 
it  made  40,  it  was  diminished  about  \  :  when  it  made 
less  than  18|,  its  motion  was  irregular  ;  and  when  it  was 
loaded  so  as  not  to  admit  its  making  18  turns,  the  wheel 
was  overpowered  by  its  load. 

It  is  an  advantage  in  jiractice,  that  the  velocity  of  the 
wheel  should  not  be  diminished  farther  than  what  will 
procure  some  solid  advantage  in  point  of  power;  be- 
cause, as  the  motion  is  slower,  the  buckets  must  be 
made  larger:  and  the  wheel  being  more  loaded  with 
water,  the  stress  upon  every  part  of  the  work  will  be 
increased  in  propordon  :  the  best  velocity  for  practice, 
therefore,  will  be  such  as  when  the  wheel  here  used 


144  HYDRAULICS.  [Chap.  12. 

made  about  SO  turns  in  a  minute  ;  that  is,  when  the  ve- 
locity of  tlie  circumference  is  a  little  more  than  3  feet  in 
a  second. 

Experience  confirms,  that  this  velocity  of  3  feet  in  a 
second,  is  applicable  to  the  highest  overshot  wheels  as 
well  as  the  lowest ;  and  all  other  parts  of  the  work  being 
properly  adapted  thereto,  will  produce  very  nearly  the 
greatest  effect  possible.  However,  this  also  is  certain, 
from  experience,  that  high  wheels  may  deviate  further 
from  this  rule,  before  they  will  lose  their  power,  by  a 
given  aliquot  part  of  the  whole,  than  low  ones  can  be 
admitted  to  do  ;  for  a  wheel  of  24  feet  high  may  move 
at  the  rate  of  6  feet  per  second  without  losing  any  con- 
siderable part  of  its  power :  and,  on  the  other  hand,  I 
have  seen  a  wheel  of  33  feet  high  that  has  moved  very 
steadily  and  well,  with  a  velocity  but  little  exceeding  2 
feet.* 

[Said  Smeaton  has  also  made  a  model  of  a  wind-mill, 
and  a  complete  set  of  experiments  on  the  power  and 
effect  of  the  wind,  acting  on  wind-mill  sails  of  different 
constructions.  But  as  the  accounts  thereof  are  quite  too 
long  for  the  compass  of  my  work,  I  therefore  only  ex- 
tract little  more  than  a  few  of  the  principal  maxims  de- 
duced from  his  experiments,  which,  I  think,  may  not 
only  be  of  good  sei-vice  to  those  who  are  concerned  in 
building  wind-mills,  but  may  serve  to  confirm  some 
principles  deduced  from  his  experiments  on  water- 
mills.] 


ART.  69. 

PART  III. 

ON  THE  CONSTRUCTION  AND  EFFECTS  OF  WIND-MILL  SAILS.t 

In  trying  experiments  on  wind-mill  sails,  the  wind 
itself  is  too  uncertain  to  answer  the  purpose ;  we  must 
therefore  have  recourse  to  artificial  wind. 

•  Probably  this  wheel  was  working  a  forge  or  furnace  bellows,  which 
have  deceived  many  by  their  slow  regular  motion. 

t  Read  May  31st  and  June  14th,  1759,  in  the  Philosophical  Society  of 
Tendon. 


Ghap.  12.] 


HYDRAULICS. 


145 


This  may  be  done  two  ways ;  either  by  causing  the 
air  to  move  against  the  machine,  or  the  machine  to  move 
against  the  air.  To  cause  the  air  to  move  against  the 
machine  in  a  sufficient  column,  with  steadiness  and  the 
requisite  velocity,  is  not  easily  put  in  practice  :  To  car- 
ry the  machine  forward  in  a  right  line  against  the  air, 
would  require  a  larger  room  than  I  could  conveniently 
meet  with.  What  I  found  most  practicable,  therefore, 
was  to  carry  the  axis  whereon  the  sails  were  to  be  fixed 
progressively  round  in  the  circumference  of  a  large 
circle.     Upon  this  idea  the  machine  was  constructed.* 

Specimen  of  a  Set  of  Experiments. 

Radius  of  the  sails,         ...         - 

Length  of  do.  in  cloth,         ... 

Breadth  of  do. 
(  Angle  at  the  extremity, 

f  <  Do.  at  the  greatest  inclination, 
(  20  turns  of  the  sails  raised  the  weight. 

Velocity  of  the  centre  of  the  sails  in  the  cir- 
cumference of  the  great  circle  in  a  second, 
in  which  the  machine  was  carried  round, 

Continuance  of  the  experiment, 

No'      Weight  in  the  scale.        Turns. 

1  Olb.  108 

2  6  85 

3  6|  81 

4  7  78 

5  71  73 

6  8  65 

7  9  0 

The  product   is  found  by   simply  multiplying  the 
weight  in  the  scale  by  the  number  of  turns. 

•  I  decline  p^iving  any  description  or  draught  of  this  machine,  as  I  have 
not  room  ;  but  I  may  say,  that  it  was  constructed  so  as  to  wind  up  a 
weight,  (as  did  the  other  model)  in  order  to  find  the  effect  of  the  power.' 
I  may  also  insert  a  specimen  of  a  set  of  experiments,  which  I  fear  will  not 
be  well  understood  for  want  of  a  full  explanation  of  the  machine. 

t  In  the  following  experiments,  the  angle  of  the  sail  is  accounted  from 
the  plain  of  their  motion  ;  that  is,  when  they  stand  at  right  angles  to  the 
axis,  their  angle  is  denoted  °  deg. ;  this  notation  being  agreeable  to  the 
language  of  practitioners,  who  call  the  angle  so  denoted  the  weather  of  the 
sail ;  which  they  denominate  greater  or  less,  according  to  the  quantity  of 
the  angle. 


21  inches 
18 
5,6 

10  degs. 
25 
11,3  inch. 

6  feet. 


52  seconds 

Product. 

0 
510 

526| 
546 

5*7 1  maxim. 
520 
0 


146  HYDRAULICS.  [Chap.  12. 

By  this  set  of  experiments  it  appears,  that  the  maxi- 
mum velocity  is  2-3  of  the  greatest  velocity,  and  that 
the  ratio  of  the  greatest  load  to  that  of  a  maximum  is,  as 
9  to  7,5,  but  by  adding  the  weight  of  the  scale  and  fric- 
tion to  the  load,  the  ratio  turns  out  to  be  as  10 :  8,4,  or  as 
5  to  4,  nearly.  The  following  table  is  the  result  of  19 
similar  sets  of  experiments. 

By  the  following  table  it  appears,  that  the  most  gene- 
ral ratio  between  the  velocity  of  the  sails  unloaded  and 
when  loaded  to  a  maximum,  is  3  to  2,  nearly. 

And  the  ratio  between  the  ijreatest  load  and  the  load 
at  a  maximum  (taking  such  experiments  where  the  sails 
answered  best),  is  at  a  medium  about  as  6  to  5,  nearly. 

And  that  the  kind  of  sails  used  in  the  15th  and  16th 
experiments  are  best  of  all,  because  they  produce  the 
greatest  effect  or  product,  in  proportion  to  their  quantity 
of  surface,  as  appears  in  column  12. 


Xhap.  12j 


HYDRAULICS. 


ur 


TABLE  IV. 


Containing  Nineteen  Sets  of  Experiments  on  Wind-mill  Sails  of  varioug 
Structures,  Positions,  and  Quantities  of  Surface. 


H 

z    > 

O 

H 

H 

r 

7i 

-3 

g> 

jg 

BJ 

7S 

3 

-» 

p 

n 

3 

n 

>5 

-J 

3 

s 

n 

V 

o 

p 

3 

«  5" 

5 

o 

5* 

3- 
t 
■5 

V 

to 

n 

c 

is, 

S  5- 

o 

3 

^ 

3 

-n 

0) 

n 

e/q. 

a 

3 

p. 

c 

v:  at; 

^"S 

p-  = 

»9 

T 

3  fD 

to 

-> 
n 

w 

i" 

s 

S  p 

3 
a. 

3. 

5 

c 
3 

3 

3  S 

3  Z 

C    o 

o 

n 

Ul 

» 

3  o 

.=^S. 

C. 

c 

• 

c  9. 

r^ 

n 

fi> 

3^ 

"O 

o 

.-» 

•^ 

7»» 

1 

1 

2 

0 

35 

12 

0 

35 
12 

66 

42 
70 

lb. 
7,56 

o 

n 

• 

lb. 
12,59 

318 
441 

sq.in 
404 
404 

10:7 

10:6 

10:  7,  9 

6,3 

7,56 

10:8,3 

10:10,  1 

II. 

3 

15 

15 

105 

69 

6.72 

8,12 

464 

404 

10:6,6 

10:8,3 

10:10.15 

4 
5 

18 
9 

18 
26,5 

96 

66 

7,0 

9,81 

462 
462 

404 
404 

10:7 

10:7.1 

10:10,15 

66 

7,0 

10:11,  4 

III. 

6 

12 

29,5 

70,5 

7,35 

518 

404 

10:12,  8 

7 
8 

15 
0 

32,5 
15 

,63,5 
120  93 

8,3 
4,75 

5,31 

527 

442 

404 

10:13,  0 

404 

10:7,7 

10:8,9 

10  11,  0 

9 

o 

18 

120  79 

7,0 

8.12 

553 

404 

10:6,6 

10:8.6 

10:13,  7 

IV. 

10 

5 

20 

78 

7,5 

8,12 

585 

404 

10:9,2 

10:14.  5 

11 

7,5 

22.5 

113  77 

8,3 

9,81 

639 

404 

10:6,8 

10:8  5 

10:15,  8 

12 

10 

25 

108  73 

8.69 

10,37 

634 

404|10:^,8 

10:8.4  10:15,  7 

13 
14 

12 
7,5 

27 
22.5 

10066 
123  75 

8  41 
10,65 

10,94 

580 

404'10.6,6 

10:7,7  il0:14,  4 

12,59 

799 

505,10:6,1 

10:8,5 

10:15.  8 

V 

15 

10 

'25 

117  74 

11.08 

13,69 

820 

505  10:6  3 

10:8,1 

10:16,  2 

16 

12 

27 

114  66 

12.09 

14,23 

799 

.i05 

10:5.8 

10.8,4 

10:15,  8 

VI 

17 
18 

15 
12 

30 
22 

96  63 
10564,5 

12,09 
16,42 

14,78 
27,87 

762 

505 

10:6,6 

10:8,2  10:15,  1 

1059 

854 

10:6,1 

10:5,9  10:12,  4 

19 

1 

12 
2 

22 

99.64,5 

18.06 
6 

7 

1165 
8 

1146 

10:5,9 

f]0:IO,  1 

^ 

1 

4 

5 

9 

10 

11     12 

I.  Plain  sails  at  an  angle  of  55  degrees. 

II.  Plain  sails  weathered  according  to  common  practice- 
IIL   Weathered  according  to  Muclaurin's  theorem. 

IV-  Weathered  in  the  Dutch  manner,  tried  in  various  positions. 

V-  Weathered  in  the  Dutch  manner,  but  enlarged  towards  the  extre- 
mities. 

VI.  8  sails,  being'  sectors  of  ellipses  in  their  best  positions. 


He 


HYDRAULICS. 


[Chap.  12. 


TABLE  V. 


Containing-  the  Result  of  6  Sets  of  Experiments,  made  for  determining  the 
difference  of  Effect  according  to  the  difference  of  >he  Wind. 


Ratio  of  the  greatest  load  to  the  load 
at  a  maximum- 

CO  .-<_ 

CO  oi 

o  o 

10:8.5 
10:8,7 

Ratio  of  the  greatest  velocity  to  the 
velocity  at  a  maximum. 

o  o 

o  o 

,-r->      1 

CO 

Ratio  of  the  two  products  .     .     .     . 

2 

CO 
O 

o 

S 

Product  of  the  lesser  luad  and  great- 
er velocity. 

o 
00 

o 
00 

1-( 

CO 

00 

CJi 

= 

Turns  of  the  sails  therewith  .     .     . 

o 

00 

CO 

o 

Maximum  load  for  the  half  velocity. 

CO 

o 

o> 

>C  CI 

O  00 
O  I^ 
CO  •>! 

o  ■* 

CO  o 

00 

Greatest  load 

_2 

CO  C5^ 
>r;'  Qo" 

00  CO 
CM 

K 

Load  at  the  maximum    ..... 

£_ 

CO  '-H 
vi  00 

Turns  of  the  sails  at  a  maximum 

(C  CO 

S2 

Iv.rns  of  the  sals,  unloaded    .     .     . 

1     C   l^ 

a-,  o 

Velocity  of  the  wind  in  a  second 

c 

T^l   00 

-^  00 

V5 

'^  Ol 
■<J"  00 

CO 

1  Angle  at  the  extremity       .... 

5: 

in  V) 

»0  'TS 

o  o 

<M 

1  Number , 

f  c^ 

CO  'i- 

«n  VO 

i-t 

N  B-  The  sails  were  the  same  kind  as  those  of  Nos.  10,  11  and  12,  table 
IV.    Continuance  of  the  experiment  one  minute- 


Chap.  12.]  HYDRAULICS.  149 

Concerning  the  Effects  of  Sails  according  to  the  different 
Velocity  of  the  fVind, 

From  the  foregoing  table  the  following  maxims  are  de- 
duced. 

Maxim  I.  The  velocity  of  wind-mill  sails,  whether 
unloaded  or  loaded,  so  as  to  produce  a  maximum,  is 
nearly  as  the  velocity  of  the  wind,  their  shape  and  posi- 
tion being  the  same. 

This  appears  by  comparing  the  respective  numbers 
of  columns  4  and  5,  table  V,  wherein  those  numbers  2, 
4  and  6,  ought  to  be  double  of  No.  1,  3  and  5,  and  are 
as  nearly  so  as  can  be  expected  by  the  experiments. 

Maxim  II.  The  load  ai  the  maximum  is  nearly  but 
somewhat  less  than  as  the  square  of  the  velocity  of  the 
wind,  the  shape  and  position  of  the  sails  being  the  same. 
This  appears  by  comparing  No.  2,  4  and  6,  in  column 
6,  with  1,  3  and  5,  wherein  the  former  ought  to  be  quad- 
ruple of  the  latter  (as  the  velocity  is  double)  and  are  as 
nearly  so  as  can  be  expected. 

Maxim  III.  The  effects  of  the  same  sails  at  a  maxi- 
mum are  nearly,  but  somewhat  less  than,  as  the  cubes 
of  the  velocity  of  the  wind.* 

It  has  been  shewn,  maxim  I,  that  the  velocity  of  sails 
at  a  maximum,  is  nearly  as  the  velocity  of  the  wind ; 
and  by  maxim  II,  that  the  load  at  the  maximum  is 
nearly  as  the  square  of  the  same  velocity.  If  those  two 
maxims  would  hold  precisely,  it  would  be  a  consequence 
that  the  effect  would  be  in  a  triplicate  ratio  thereof. 
How  this  agrees  with  experiment  will  appear  by  com- 
paring the  products  in  column  8,  wherein  those  of  No. 
2,  4  and  6  (the  velocity  of  the  wind  being  double) 
ought  to  be  octuble  of  those  of  No.  1,  3  and  5,  and  are 
nearly  so. 

Maxim.  IV.  The  load  of  the  same  sails  at  the  maxi- 
mum is  nearly  as  the  squares  of,  and  their  effects  as  the 
cubes  of,  their  number  of  turns  in  a  given  time. 

This  maxim  may  be  esteemed  a  consequence  of  the 
hree  preceding  ones. 

•  This  confirms  the  7th  law  of  spouting  fluids. 

i 


150  HYDRAULICS.  [Chap.  12. 

[These  4  maxims  agree  with  and  confirm  the  4  max- 
ims concerning  the  effects  of  spouting  fluids  acting  on 
undershot  mills  :  and,  I  think,  sufficiently  confirms  as  a 
law  of  motion,  that  the  effect  produced,  if  not  the  instant 
momentum  of  a  body  in  motion,  is  as  the  square  of  its 
velocity,  as  asserted  by  the  Dutch  and  Italian  philoso- 
phers. 

Smeaton  says,  that  by  several  trials  in  large,  he  has 
found  the  following  angles  to  answer  as  well  as  any  :] 
The  radius  is  supposed  to  be  divided  into  6  parts,  and 
1-6  reckoning  from  the  centre  is  called  1,  the  extremity 
being  denoted  6. 


No, 

Angle  with  the  a'Kis. 

Angle 

with  the  plain  of  motion. 

1 

72° 

18° 

2 

71 

19 

3 

72 

18  middle. 

4 

74 

16 

5 

771 

121 

6  83  7  extremity. 

[He  seems  to  prefer  the  sails  being  largest  at  the  ex- 
^emities.] 


END  OP  PART  FIRST 


PART  II. 


THE  YOUNG 
MILL-WRIGHT'S  GUIDE. 


-f;ff  .rrr/ 


INTRODUCTION. 


WHAT  has  been  said  in  the  first  part,  was 
meant  to  establish  theories  and  easy  rules.  In 
this  part  I  mean  to  bring  them  into  practice,  in 
as  concise  a  manner  as  possible,  referring  only 
to  the  articles  in  the  first  part,  where  the  rea- 
sons and  demonstrations  are  given. 

This  part  is  particularly  intended  for  the  help 
of  young  and  practical  mill-wrights,  whose  time 
will  not  permit  them  fully  to  investigate  the  prin- 
ciples of  theories,  which  require  a  longer  series 
of  studies  than  most  of  them  can  possibly  spare 
from  their  business  ;  therefore  I  shall  endeavour 
here  to  reduce  the  substance  of  all  that  has  been 
said,  to  a  few  tables,  rules,  and  short  directions, 
which,  if  found  to  agree  with  practice,  will  be 
sufficient  for  the  practitioner. 

There  are  but  two  principles  by  which  water 
acts  on  mill-wheels,  to  give  tJiem  motion,  viz. 
Percussion  and  Gravity. 


154  INTRODUCTION. 

That  equal  quantities  of  water,  under  equal 
perpendicular  descents,  will  produce  double  the 
power  by  gravity  that  they  will  by  percussion,  has 
been  shown  in  articles  8  and  68. 

Therefore,  when  the  water  is  scarce,  we  ought 
to  endeavour  to  cause  it  to  act  by  gravity  as  much 
as  possible,  paying  due  regard  to  other  circum- 
stances noted  in  article  44,  so  as  to  obtain  a  steady 
motion,  §c.  .i    u       ,:> 


■  ■  ;  >  i  ■ . 

.     .     il!V,' 


.v.tiv'ij'iO  ba&  itoigajjo ,  '  \ 


THE 

YOUNG  MILL-WRIGHT'S 
GUIDE. 


PART  THE  SECOND. 


CHAPTER  L 

OF  THE  DIFFEHENT  KINDS  OF  MILLS 


ARTICLE    70. 

OF  UNDERSHOT  MILLS. 

UNDERSHOT  wheels  move  by  the  percussion  oi: 
stroke  of  the  water,  and  are  only  half  as  powerful  as 
Other  wheels  that  are  moved  by  the  gravity  of  the  wa- 
ter. See  art.  8.  Therefore  this  construction  ought  not 
to  be  used,  except  where  there  is  but  little  fall  or  great 
plenty  of  water.  The  undershot  wheel,  and  all  others 
that  move  by  percussion,  should  move  with  a  velocity 
nearly  equal  to  two-thirds  of  the  velocity  of  the  water. 
See  art.  42.  Fig.  28,  plate  IV.  represents  this  construc- 
tion. 

For  a  rule  for  finding  the  velocity  of  the  water,  under 
any  given  head,  see  art.  51. 

Upon  which  principles,  and  by  said  rule,  is  formed 
the  following  table  of  the  velocity  of  spouting  water, 
under  different  heads,  from  one  to  twenty-five  feet  high 
above  the  centre  of  the  issue  ;  to  which  is  added  the 
velocity  of  the  wheel  suitable  thereto,  and  the  number 
of  revolutions  a  wheel  of  fifteen  feet  diameter  (which  I 
take  to  be  a  good  size)  will  revolve  in  a  minute :  also, 


156  HYDRAULICS.  [Chap.  12. 

the  number  of  cogs  and  rounds  in  the  wheels,  both  for 
double  and  single  gears,  so  as  to  produce  about  ninety- 
seven  or  one  hundred  revolutions  for  a  five  feet  stone  per 
minute,  which  I  take  to  be  a  good  motion  and  size  for  a 
mill-stone,  grinding  for  merchantable  ftour. 

That  the  reader  may  fully  understand  how  the  follow- 
ing table  is  calculated,  let  him  observe, 

1.  That  by  art.  42,  the  velocity  of  the  wheel  must  be 
just  577  thousandth  parts  of  the  velocity  of  the  water ; 
therefore  if  the  velocity  of  the  water,  per  second,  be 
multiplied  by  ,577  the  product  will  be  the  maximum 
velocity  of  the  wheel,  or  velocity  that  will  produce  the 
greatest  effect,  which  is  the  third  column  in  the  table. 

2.  The  velocity  of  the  wheel  per  second,  multiplied 
by  60,  produces  the  distance  the  circumference  moves 
per  minute,  which  divided  by  47,1  feet,  the  circumfe- 
rence of  a  15  feet  wheel,  quotes  the  number  of  revolu- 
tions of  the  wheel  per  minute,  which  is  the  fourth  column^ 

3.  That  by  art.  20  and  74,  the  number  of  revolutions 
of  the  wheel  per  minute,  multiplied  by  the  number  of 
cogs  in  all  the  driving  wheels,  successively,  and  that 
product  divided  by  the  product  of  the  number  of  cogs 
in  all  the  leading  wheels,  multiplied  successively,  the 
quotient  is  the  revolutions  of  the  stones  per  minute, 
which  is  the  ninth  and  twelfth  columns. 

4.  The  cubochs  of  power  required  to  drive  the  stone, 
being,  by  art.  61,  equal  to  111,78  cubochs  per  second, 
which,  divided  by  half  the  head  of  water,  added  to  all 
tlie  fall  (if  any),  being  the  virtual  or  effective  head  by 
art.  61,  quotes  the  quantity  of  water,  in  cubic  feet,  re- 
quired per  second,  which  is  the  thirteenth  column. 

5.  The  quantity  required,  divided  by  the  velocity  with 
which  it  is  to  issue,  quotes  the  area  of  the  aperture  of  the 
gate — fourteenth  column. 

6.  The  quantity  required,  divided  by  the  velocity  of 
the  water  proper  for  it  to  move  along  the  canal,  quotes 
the  area  of  the  section  of  the  canal — fifteenth  column. 

7.  Having  obtained  their  areas,  it  is  easy,  by  art.  65, 
to  determine  the  width  and  depth,  as  may  suit  other 
circumstances. 


Chap.  1.] 


OF  UNDERSHOT  MILLS. 


157 


THE  MILLWRIGHT'S  TABLE 


UNDERSHOT  MILLS, 

CALCULATED  FOR  A  WATER-WHEEL  OF  FIFTEEN  FEET,  AND 
STONES  OF  FIVE  FEET  DIAMETER. 


[3;; 

< 

t 

n 

a 

o 
o 

o 

^' 

"^' 

«< 

5 

o 

n 

O    S" 

-•  n 

"  n 

— .  T 

^ 

3t3 

^ 

-3  n 

■3 

P   -s 

2.  " 

O 

o 

o 

3 

3 

*^ 

& 

O 

P 

^^. 

». 

^ 

=J 

feet. 

feet. 

p  n> 
p  ^ 

If 

3"    en 


2; 

c 

_3 

p'5 
3  S- 


feel. 


1 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 


8,1 
11,4 
14, 
16,2 
18, 
19,84 
21,43 
22,8 
24,3 
25,54 
26,7 
28, 
29,16 
30,2 
31,34 
32,4 
33,32 
34,34 
35,18 
36,2 
37.11 
37,98 
38,79 
39,6S 
40,5 

2 


4,67 
6,57 
8,07 


5,94 

8,36 

10,28 


9,3411,19 
10,3813,22 
11,441 14,6 
12,36!l5,74i 


Il2i22  54 


96'23 
88'2o 
78  23 
66  24 

6612448 
66I2544 


13,15 
14,02 
14,73 
15.42 
16,16 
16.82 
17,42 
18,08 
18,69 
19,22 
19,81 


16,75 
17,86 
18,78 
19,7 
20,5 
21,42 
22,19 
23,03 
23,8 
24,48 
25,23 
0,29j2j,82 
20,88126,6 
21,4127,26 
21,86  27,84 
22,38  28,5 
22,9   29,17 
23,3629,75 


66:25 
66I26 
60;25 
6026 


29 


101,6 
99, 

100,5 
97, 
97, 
96,2 
96,2 
97,2 

100,2 
99, 

100, 

100, 
99,8 
99, 
99, 


112 
112 

104 
96 
96 
96 
96 
96 
96 


a 


!"    i- 
"^^ 


t/5  rt 
r»  ft, 
2U2 


a  "5 


=■0 


o  5- 


«  S  ^ 


f  rf  "^ 
5  O  '» 
'T)    ^    p 

o"  O-  O 
O    -1    -»: 

—  5"  p 

a> 
C    o 

3    C. 


p   cr 


cub.  ft. 


10    11 


sup.  fl 


98,66 

96,2 

96,2 

100, 

100,8 

100, 
99,5 
98.4 

102,6 
97,63 
96,5 
99,7 
97,9 
96,1 
98  3 
98,3 
97, 
98.6 
97,7 
96,2 
99, 

12 


^  '^  S" 

O    ^ 

3  1 


223,5 

111,78 

74,52 

55,89 

44,7 

37,26 

31,9 

27,94 

24,84 

22,89 

20,32 

18,63 

16,27 

15,94 

14,9 

13,97 

13.14 

12,42 

11,76 

11,17 

10,64 

10,16 

9.72 

9,32 

8,94 

13 


?  3 


sup.  ft. 


27,5 
98 
4,6 
3,45 
2.48 
1,9  I 
1,48 
122 
1,02 
,9 
,76 
,66 
,56 
,53 
,47 
,43 
,39 
,36 
,3: 
,3 
,29 
,26 
.25 

TJ 
,^0 

,22 


14 


149, 
74.5 

43; 
37,26 
29,8 
24,84 
21,26 
18,6 
16,56 
15,26 
13,54 
12,42 
10,8 
10,6 
9,93 
9.31 
8,76 
8,28 
784 
7.4 
7,1 
6.7/ 
6,48 
6.21 
5,96 

15 


158  OF  UNDERSHOT  MILLS.  [Chap.  1. 

Note,  that  five  feet  fall  is  the  least  that  a  single  gear 
can  be  built  on,  to  keep  the  cog-wheel  clear  of  the  water, 
and  give  the  stone  sufficient  motion. 

Although  double  gear  is  calculated  to  fifteen  feet  fall, 
yet  I  do  not  recommend  them  above  ten  feet,  unless  for 
some  particular  convenience,  such  as  two  pair  of  stones 
to  one  wheel,  &c.  &c.  The  number  of  cogs  in  the  wheels 
are  even,  and  chosen  to  suit  eight,  six,  or  four  arms,  so 
as  not  to  pass  through  any  of  them,  this  being  the  com- 
mon practice.  But  when  the  motion  cannot  be  obtained 
without  a  trundle  that  will  cause  the  same  cogs  and 
rounds  to  meet  too  often,  such  as  16  into  96,  which  will 
meet  every  revolution  of  the  cog-wheel,  or  18  into  96, 
which  will  meet  every  third  revolution — I  advise  rather 
to  put  in  one  more  or  less,  as  may  best  suit  the  motion, 
which  will  cause  them  to  change  oftener.     See  art.  82. 

Note,  that  the  friction  at  the  aperture  of  the  gate  will 
greatly  diminish  both  the  velocity  and  power  of  the  wa- 
ter in  this  application,  where  the  head  is  great,  if  the 
gate  be  made  of  the  usual  form,  wide  and  shallow. 
Where  the  head  is  great,  the  friction  will  be  great.  See 
art.  55.  Therefore  the  wheel  must  be  narrow,  and  the 
aperture  of  the  gate  of  a  square  form,  to  evade  the  fric- 
tion and  loss  that  may  be  under  a  wide  wheel,  if  it  does 
not  run  close  to  the  sheeting. 

Use  of  the  Table. 

Having  levelled  your  mill-seat  carefully,  and  finding 
such  fall  and  quantity  of  water  as  determines  you  to 
make  choice  of  an  undershot  wheel ;  for  instance,  sup- 
pose 6  feet  fall,  and  about  45  cubic  _  feet  of  water  per 
second,  which  you  find  as  directed  in  art.  So',  cast  oft" 
about  1  foot  for  fall  in  the  tail-race,  below  the  bottom  of 
the  wheel,  if  subject  to  back-water,  leaves  you  5  feet 
head ;  look  for  five  feet  head  in  the  first  column  of  the 
table,  and  against  it  are  all  the  calculations  for  a  15  feet 
water-wheel  and  5  feet  stones ;  in  the  thirteenth  column 
you  have  44,7  cubic  feet  of  water;  which  shews  you 
have  enough  for  a  five  feet  pair  of  stones  j  and  the  velocity 


Chap.  1.]        OF  UNDERSHOT  MILLS.  159 

of  the  water  will  be  18  feet  per  second,  the  velocity  of  the 
wheel  10,38  feet  per  second,  and  it  will  revolve  13,22 
times  per  minute.  And  if  you  choose  double  gear,  then 
66  cogs  in  the  master  cog-wheel,  24  rounds  in  the  wal- 
lower,  48  cogs  in  the  counter  cog-wheel,  and  18  rounds 
in  the  trundle,  will  give  the  stone  97  revolutions  in  a 
minute;  if  single  gear,  112  cogs  and  15  rounds  give 
98,66  revolutions  in  a  minute ;  it  will  require  44,7  cubic 
feet  of  water  per  second ;  the  size  of  the  gate  must  be 
2,48  feet,  which  will  be  about  4  feet  wide  and  ,62  feet 
deep,  about  71  inches  deep  ;  the  size  of  the  canal  must 
be  29,8  feet;  that  is,  about  3  feet  deep,  and  9,93  or  nearly 
10  feet  wide.  If  you  choose  single  gear,  you  must  make 
your  water-wheel  much  less,  say  7|  feet,  the  half  of  15 
feet,  then  the  cog-wheel  must  have  half  the  number  of 
cogs,  the  trundle-head  the  same,  the  spindle  will  be 
longer,  husk  lower,  and  the  mill  full  as  good ;  but  in  this 
case,  it  will  not  do,  because  a  cog-wheel  of  66  cogs  would 
reach  the  water ;  but  where  the  head  is  10  or  12  feet,  it 
will  do  very  well. 

If  you  choose  stones,  or  water-wheels,  of  other  sizes, 
it  will  be  easy,  by  the  rules  by  which  the  table  is  calcu- 
lated, to  proportion  the  whole  to  suit,  seeing  you  have 
the  velocity  of  the  periphery  of  a  wheel  of  any  size.* 

*  One  advantag'e  large  wheels  have  over  small  ones  is,  they  cast  off  the 
back-water  much  better.  The  buckets  of  the  low  wheel  will  lift  the  water 
much  more  than  those  of  the  high  wheel ;  because  the  nearer  the  water 
rises  to  the  centre  of  the  wheel,  the  nearer  the  buckets  approach  the  ho- 
rizontal or  lifting  position. 

To  make  a  wheel  cast  off  back-water,  fix  tlie  sheeting  below  the  wheel, 
with  joints  and  hinges,  so  that  the  end  down  stream  can  be  raised  to  shoot 
the  water  as  it  leaves  the  wheel  on  the  surface  of  the  backwater,  to  roll 
it  from  the  wheel,  and  it  will  drive  off  the  back-water  much  better.  So 
says  Adrian  Dawes,  mill-wright,  Jersey. 

Plate  IV.  Fig.  28,  is  an  undershot  wheel-  Some  prefer  to  slant  the  fore- 
bay  under  the  wheel,  as  in  the  figure,  that  the  gate  may  be  drawn  near  the 
floats ;  because  (say  they)  the  water  acts  with  more  power  near  the  gate, 
than  at  a  distance;  which  appears  to  be  the  case,  when  we  consider,  that 
the  nearer  we  approach  the  gate,  the  nearer  the  column  of  water  approaches, 
to  be  what  is  called  a  perfect  definite  quantity.     See  art.  59. 

Others  again  say,  that  it  acquires  equal  power  io  descending  the  shute 
(it  will  certainly  acquire  equal  velocity  abating  only  for  the  friction  of  the 
shate  and  air.)  When  the  shute  has  a  considerable  descent,  the  greater 
the  distance  from  the  gate,  the  greater  the  velocity  and  power  of  the  water; 
but  where  the  descent  of  the  shute  is  not  sufficient  to  overcome  the  friction 
of  the  air,  &c.  then  the  nearer  the  gate,  the  greater  t-he  velocity  and  power 


160  OF  TUB  MILLS.  [Chap.  1. 

Obsei-vations  on  the  Table. 

1.  It  is  calculated  for  an  undershot  wheel  constructed, 
and  the  water  shot  on,  as  in  plate  IV,  fig.  28.  The  head 
is  counted  from  the  point  of  impact  I,  and  the  motion  of 
the  wheel  at  a  maximum,  about  ,58  of  the  velocity  of 
the  water  ;  but  when  there  is  plenty  of  water,  and  great 
head,  the  wheel  will  run  best  at  about  ,66  or  two-thirds 
of  the  velocity  of  the  water ;  therefore  the  stones  will 
incline  to  run  faster  than  in  the  table,  in  the  ratio  of  58 
to  66,  nearly ;  for  which  reason,  I  have  set  the  motion  of 
5  feet  stones  under  100  revolutions  in  a  minute,  which  is 
slower  than  common  practice  ;  they  will  incline  to  run 
between  96  and  110  revolutions. 

2.  I  have  taken  half  of  the  whole  head  above  the  point 
of  impact,  for  the  virtual  or  effective  head,  by  art.  53  ; 
which  appears  to  me  will  be  too  little  in  very  low  heads, 
and  perhaps  too  much  in  high  ones.  As  the  principle 
of  non-elasticity  does  not  appear  to  me  to  operate  against 
the  power  so  much  in  low  as  in  high  heads,  therefore 
if  the  head  be  only  1  foot,  it  may  not  require  223,5 
cubic  feet  of  water  per  second,  and  if  20  feet,  may  re- 
quire more  than  11,17,  cubic  feet  of  water  per  second, 
as  in  the  table.     See  art.  8. 


ART.    71. 
OF  TUB  MILLS. 

A  tub  mill  has  a  horizontal  water-wheel,  that  is  acted 
on  by  the  percussion  of  the  water  altogether ;  the  shaft 

of  the  water  ;  which  argues  in  favour  of  drawing  the  gate  near  the  floats. 
Yet,  wl>ere  the  tall  is  great,  or  water  plenty,  and  the  expense  of  a  deep 
penstock  considerable,  tlie  small  difference  of  power  is  not  wortii  the  ex- 
pense of  obtaining.  In  these  cases,  it  is  best  to  have  a  shallow  penstock, 
and  a  long  shute  to  convey  the  water  down  to  the  wheel,  drawing  the  gate 
at  the  top  of  the  shnte:  which  is  frequently  done  to  save  expense,  in  build- 
ing saw-mills,  with  flutter-wheels,  which  are  small  undershot  wheels,  fixed 
on  the  crank,  so  small  as  to  obtain  a  suflScient  number  of  strokes  of  the  saw 
in  a  minute,  say  about  120.  This  wheel  is  to  be  calculated  of  such  a  size 
as  to  suit  the  velocity  of  the  water  at  the  point  of  impact,  so  as  to  make 
that  number  of  revolutions  in  a  minutes. 

For  the  method  of  shooting  the  water  on  an  undershot  wheel,  where  the 
fall  is  great,  see  Thomas  EUicott's  plan,  part  5,  plate  I,  fig.  6. 


€hap.  1.]  OF  TUB  MILLS.  161 

is  vertical,  carrying  the  stone  on  the  top  of  it,  and  serves 
in  place  of  a  spindle  ;  die  lower  end  of  this  shaft  is  set 
in  a  step  fixed  in  a  bridge-tree,  by  which  the  stone  is 
raised  and  lowered,  as  by  the  bridge-tree  of  other  mills ; 
the  water  is  shot  on  the  upper  side  of  the  wheel,  in  a 
tangent  direction  with  its  circumference.  See  fig.  29, 
plate  IV,  which  is  a  top  view  of  the  tub- wheel,  and  fig. 
30  is  a  side  view  of  it,  with  the  stone  on  the  top  of  the 
shaft,  bridge- tree,  &c.  The  wheel  runs  in  a  hoop,  like 
a  mill-stone  hoop,  projecting  so  far  above  the  wheel  as 
to  prevent  the  water  from  shooting  over  the  ^^heel,  and 
■whirls  it  about  until  it  strikes  the  buckets,  because  the 
water  is  shot  on  in  a  deep  narrow  column,  9  inches  wide 
and  18  inches  deep,  to  drive  a  5  feet  stone,  with  8  feet 
head — so  that  all  this  column  cannot  enter  the  buckets 
until  part  has  passed  half  way  round  the  wheel,  so  that 
there  are  always  nearly  half  the  buckets  struck  at  once ; 
the  buckets  are  set  obliquely,  so  that  the  water  may 
strike  them  at  right  angles.  See  Plate  IV.  fig.  30.  As 
soon  as  it  strikes  it  escapes  under  the  wheel  in  every  di- 
rection, as  in  fig.  S9.* 

*  Note,  That  in  plate  IV.  fip;.  30,  I  have  allowed  the  gate  to  be  drawn 
inside  of  the  penstock,  and  not  in  the  shute  near  the  wheel,  as  is  the  com- 
mon practice;  L)eca  ise  the  water  will  leak  out  much  along  side  of  the  gate, 
if  drawn  in  the  shute  But  here  we  must  consider,  that  the  gate  must' 
always  be  full  drawn  and  the  quantity  of  water  regulated  by  a  regulator 
in  the  shute  near  the  wheel;  so  that  the  shute  will  be  perfectly  full,  and 
pressed  with  the  whole  weight  of  the  head,  else  a  great  part  of  the  power 
may  be  lost. 

To  shew  this  more  plain,  suppose  the  long  shute  A,  from  the  high  head 
(shewn  by  dotted  lines)  of  the  undershot  mill,  fig.  28,  be  made  tight  by 
being  covered  at  top,  then,  if  we  draw  the  gate  A,  but  not  fully,  if  the  shute 
at  bottom  be  large  enough  to  vent  all  the  water  that  issues  through  the 
gate  when  the  shute  is  full  to  A,  then  it  cannot  fill  higher  than  A;  there- 
fore all  that  part  of  the  head  above  A  is  lost,  it  being  of  no  other  service 
than  to  supply  the  shute,  and  keep  it  full  to  A,  and  the  head  from  A  to  the 
wheel  is  all  that  acts  on  the  wheel. 

Ajj-ain,  wht-n  we  shut  the  gate,  the  shute  cannot  run  empty,  because  it 
would  leave  a  vacuum  in  the  head  of  the  shuie  at  A;  therefore  the  pressure 
of  the  atmosphere  resists  the  water  from  running  out  of  the  shute,  and 
whatever  head  of  water  is  in  the  shute,  when  the  gate  is  shut,  will  balance 
its  weight  of  the  pressure  of  the  atmosphere,  and  prevent  it  from  acting  on 
the  lower  side  of  the  gale,  which  will  cause  it  to  be  very  hard  to  draw. 
For,  suppose  11  feet  head  of  water  to  be  in  the  shute  when  the  gate  was 
shut,  its  pressure  is  equal  to  about  5  lb.  per  square  inch  ;  then,  if  the  gate 
be  48  by  6  inches,  which  is  equal  to  288  inches,  this  multiplied  by  5,  is 
equal  to  1440  lb.  the  additional  pressure  on  the  gate. 

Again,  if  the  gale  be  full  drawn,  and  the  shuie  be  not  much  larger  at 
the  upper  than  lower  end,  all  these  evils  will  take  place  to  cause  the  loss 

X 


162  OF  TUB  MILLS.  [Cliap.  1. 

The  disadvantages  of  these  wheels  are, 

1.  The  water  does  not  act  to  advantage  on  them,  we 
being  obliged  to  make  them  so  small  to  obtain  velocity 
to  the  stone  (in  most  cases)  that  the  buckets  take  up  a 
third  part  of  their  diameter. 

2.  The  water  acts  with  less  power  than  on  undershot 
wheels,  as  it  is  less  confined  at  the  time  of  striking  the 
•wheel,  and  its  non- elastic  principle  takes  place  more 
fully.     See  art.  8. 

3.  It  is  with  difficulty  we  can  put  a  sufficient  quantity 
of  water  to  act  on  them  to  drive  them  with  sufficient 
power,  if  the  head  be  low ;  therefore  I  advise  to  strike 
the  w^ater  on  in  two  places,  as  in  Plate  IV.  fig.  29  ;  then 
the  apertures  need  only  be  about  6  by  13  inches  each, 
instead  of  9  by  18,  and  will  act  to  more  advantage  ;  and 
then,  in  this  case,  nearly  all  the  buckets  will  be  acted  on 
at  once. 

Their  advantages  are. 

Their  exceeding  simplicity  and  cheapness,  having  no 
cogs  nor  rounds  to  be  kept  in  repair ;  their  wearing  parts 
are  few,  and  have  but  little  friction  ;  the  step-gudgeon 
runs  under  water,  therefore,  if  well  fixed,  will  not  get 
out  of  order  in  a  long  time  ;  and  they  will  move  with 
sufficient  velocity  and  power  with  9  or  10  feet  total  fall, 
and  plenty  of  water ;  and,  if  they  be  well  fixed,  they  will 
not  require  much  more  \Aater  than  undershot  \Aheels  ; 
therefore  they  are  vastly  preferable  in  all  seats  with 
plenty  of  water,  and  above  8  feet  fall. 

In  order  that  the  reader  may  fully  understand  how 
the  following  table  is  calculated,  let  him  consider, 

1.  That  as  the  tub-wheel  moves  altogether  by  percus- 
sion, the  water  flying  clear  of  the  wheel  the  instant  it 

of  power.  To  remedy  all  this,  put  the  gate  H  at  the  bottom  of  the  sliute 
to  regulate  the  quantity  of  water  by,  and  make  a  valve  at  A  to  shut  on  the 
inside  of  the  shute,  like  the  valve  of  a  pair  of  bellows,  which  will  shut  when 
the  gate  A  is  drawn,  and  open  when  the  gate  shu's,  to  let  air  into  the 
shute  ;  this  plan  will  do  better  than  long  open  shutes,  for  saw-mills  with 
flutter-wheels  or  tub-mills,  as  by  it  we  evade  the  friction  of  the  shute  and 
resistance  of  the  air. 

The  reader  will  with  difficulty  understand  what  is  here  said,  unless  he 
be  acquainted  with  the  theory  of  the  pressure  of  the  atmosphere,  vacuums, 
&.C.     See  these  subjects,  touched  on  in  art.  56. 


Chap.l.J  OF  TUB  MILLS.  163 

strikes,  and  it  being  better,  by  art.  70,  for  such  wheels 
to  move  faster  instead  of  slower  than  the  maximum  ve- 
locity ;  therefore,  instead  of  ,577,  we  will  allow  them  to 
move  ,66  velocity  of  the  water;  then  multiplying  the 
velocity  of  the  water  by  ,66,  gives  the  velocity  of  the 
wheel,  at  the  centre  of  the  buckets;  which  is  the  3d 
column  in  the  table. 

2.  And  the  velocity  of  the  wheel  per  second,  multi- 
plied by  60,  and  divided  by  the  number  of  revolutions 
the  stone  is  to  make  in  a  minute,  gives  the  circumference 
of  the  wheel  at  the  centre  of  the  buckets ;  which  circum- 
ference, multiplied  by  7,  and  divided  by  22,  gives  the 
diameter  from  the  centre  of  the  buckets,  to  produce  the 
number  of  revolutions  required ;  which  are  the  4th,  5th, 
6th,  and  7th  columns. 

3.  The  cubochs  of  power  required,  by  art.  63,  to  drive 
the  stone,  divided  by  half  the  head,  gives  the  cubic  feet 
of  water  required  to  produce  said  power ;  which  are  the 
8th  and  10th  columns. 

4.  The  cubic  feet  of  water,  divided  by  the  velocity, 
will  give  the  sum  of  the  apertures  of  the  gates ;  which 
are  the  9th  and  11th  columns. 

5.  The  cubic  feet  of  water,  divided  by  1,5  feet,  the 
velocity  of  the  water  in  the  canal,  gives  the  area  of  a 
section  of  the  canal;  which  are  the  12th  and  13tti 
eolumns. 

6.  For  the  quantit}'  of  water,  aperture  of  gate,  and 
size  of  canal,  for  5  feet  stones,  see  table  for  undejrshot 
mills,  in  art.  70. 


164 


OF  TUB  MILLS. 


[Ghap.  1, 


THE  MILL- WRIGHT'S  TABLE 


TUB  MILLS. 


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feet 

feet. 

fee:. 

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feet. 

feet. 

cub-  fi 

SU  It. 

cub.  ft. 

Sll.f'  . 

sup.  fi. 

sup. ft. 

8 

22.8 

15,04 

2,17 

2,73 

3,3 

3,9 

17,34 

,76 

40,9 

1.79 

11,56 

27,3 

9 

24.3 

16,03 

2,5 

3,12 

3,68 

4,37 

15,41 

,64 

36,35 

1,5 

10,3 

24,23 

10 

25,54 

16,85 

2.63 

3,28 

3.97 

4,59 

13,87 

,54 

32,72 

1,28 

9  25 

21,7 

11 

26,73 

17,64 

2,75 

3,44 

4,15 

4,8 

12,61 

,47 

29,74 

1,11 

8,4 

19,83 

12 

28, 

18,48 

2,9 

3,6 

4,34 

4,9 

11,56 

,41 

27,26 

.97 

7,7 

18.17 

13 

29,16 

19,24 

3,01 

5,74 

4,53 

.1.24 

10,67 

,36 

25,17 

.86 

7,1 

16  8 

14 

30,2 

19,93 

3,12 

3,9 

4,7 

5,43 

9,9 

,33 

23,36 

J7 

6,6 

15.56 

15 

31,34 

20,68 

3,24 

4,03 

4,87 

5.67 

9,24 

,29 

21,93 

,7 

6,16 

14,62 

16 

32,4 

21,38 

3,34 

4,12 

5,01 

5,83 

8,67 

,27 

20  45 

,6 

5,71 

13,(' 

17 

33,32 

21,99 

3,43 

4,25 

5,18 

5,95 

8,16 

,24 

19,24 

,57 

5.44 

12,15 

18 

34,34 

22,66 

3,54 

4  41 

5,32 

6,18 

7,7 

,22 

18,18 

,52 

5,13 

12,12 

19 

35,18 

23,21 

3,63 

4.52 

5,47 

6,33 

7,3 

,2 

17, 

,48 

4,9 

11,33 

20 
1 

36,2 

O 

23,89 

3,71 
4 

4,62 
5 

5.49 
6 

6,47 
7 

6,93 

,19 

16,36 

,45 

4,62 

10.9 

8 

9     1 

10 

11 

12 

13 

Chap.l.]  OF  BREAST  MILLS.  165 


Use  of  the  Table  for  Tub  Mills. 

Having  levelled  your  seat,  and  finding  that  you  have 
above  8  feet  fall,  and  plenty  of  water,  and  wish  to  build 
a  mill  on  the  simplest,  cheapest,  and  best  construction  to 
suit  your  seat,  you  will,  of  course,  make  choice  of  a  tub 
mill. 

Cast  off  1  foot  for  fall  in  the  tail-race  below  the  bot- 
tom of  the  wheel,  if  it  be  subject  to  back-water,  and  9 
inches  for  the  wheel ;  then  suppose  you  have  9  feet  left 
for  head  above  the  wheel;  look  in  the  table,  against  9 
feet  head,  and  you  have  all  the  calculations  necessary 
for  4,  5,  6,  and  7  feet  stones,  the  quantity  of  water  re- 
quired to  drive  them,  the  sum  of  the  areas  of  the  aper- 
tures, and  the  areas  of  the  canals. 

If  you  choose  stones  of  any  other  size,  you  can  easily 
proportion  the  parts  to  suit,  by  the  rules  by  which  the 
table  is  calculated. 


ART.    7S. 
OF  BREAST  MILLS- 

Breast  wheels,  which  have  the  water  shot  on  them  in 
a  tangent  direction,  are  acted  on  by  the  principles  of  both 
percussion  and  gravity;  all  that  part  above  the  point  of 
impact,  called  head,  acts  by  percussion,  and  all  that  part 
below  said  point,  called  fall,  acts  by  gravity. 

We  are  obliged,  in  this  structure  of  breast  mills,  to 
use  more  head  than  will  act  to  advantage ;  because  we 
cannot  strike  the  water  on  the  wheel,  in  a  true  tangent 
direction,  higher  than  I,  the  point  of  impact  in  Plate  IV, 
fig.  31,  which  is  a  breast-wheel,  with  12  feet  perpendicu- 
lar descent,  6,5  feet  of  which  is  above  the  point  I,  as  head, 
and  5,5  feet  below,  as  fall.  The  upper  end  of  the  shute, 
that  carries  the  water  down  to  the  wheel,  must  project 
some  inches  above  the  point  of  the  gate  when  full  drawn, 
else  the  water  will  strike  towards  the  centre  of  the 
wheel ;  and  it  must  not  project  too  high,  else  the  watei 


166  OF  BREAST  MILLS.  [Chap.  1. 

in  the  penstock  will  not  come  fast  enough  into  the  shute 
when  the  head  sinks  a  little.  The  bottom  of  the  pen- 
stock is  a  little  below  the  top  end  of  the  shute,  to  leave 
room  for  stones  and  gravel  to  settle,  and  prevent  them 
from  getting  into  the  gate. 

We  might  lay  the  water  on  higher,  by  setting  the  top 
of  the  penstock  close  to  the  wheel,  and  using  a  sliding 
gate  at  bottom,  as  shewn  by  the  dotted  lines ;  but  this 
is  not  approved  of  in  practice.  See  Ellicott's  mode, 
part  5,  plate  III,  fig.  1. 

But  if  the  water  in  the  penstock  be  nearly  as  high  as 
the  wheel,  it  may  be  carried  over,  as  by  the  upper  dotted 
lines,  and  shot  on  backwards,  making  that  part  next  the 
wheel  the  shute  to  guide  the  water  into  the  wheel,  and 
the  gate  very  narrow  or  shallow,  allowing  the  water  to 
run  over  the  top  of  it  when  drawn;  by  this  method 
(called  Pitchback)  the  head  may  be  reduced  to  the  same 
as  it  is  for  an  overshot  wheel ;  and  then  the  motion  of 
the  circumference  of  the  wheel  will  be  equal  to  the  mo- 
tion of  an  overshot  wheel,  whose  diameter  is  equal  to 
the  fall  below  the  point  of  impact,  and  their  power  will 
be  equal. 

This  structure  of  a  wheel,  Plate  IV.  fig.  31, 1  take  to 
be  a  good  one,  for  the  following  reasons,  viz. 

1.  The  buckets,  or  floats,  receive  the  percussion  of  the 
water  at  right  angles,  which  is  the  best  direction  possible. 

2.  It  prevents  the  water  from  flying  towards  the  cen- 
tre of  the  wheel,  without  re-acting  against  the  bottom  of 
the  buckets,  and  retains  it  in  the  wheel,  to  act  by  its  gra- 
vity in  its  descent,  after  the  stroke. 

3.  It  admits  air,  and  discharges  the  water  freely,  with- 
out lifting  it  at  bottom ;  and  this  is  an  important  advan- 
tage, because,  if  the  buckets  of  a  wheel  be  tight,  and  the 
wheel  wades  a  little  in  back-water,  they  will  lift  the 
water  a  considerable  distance  as  they  empty ;  the  pres- 
sure of  the  atmosphere  prevents  the  water  from  leaving 
the  buckets  freely,  and  it  requires  a  great  force  to  lift 
them  out  of  the  water  with  the  velocity  of  the  wheel; 
which  may  be  proved  by  dipping  a  common  water- 
bucket  into  water,  and  lifting  it  out,  bottom  up,  with  a 
quick  motion,  you  have  to  lift  not  only  the  water  in  the 


Chap.  1.]  OF  BREAST  MILtS.  167 

bucket,  but  it  appears  to  suck  a  deal  more  up  after  it ; 
which  is  the  effect  of  the  pressure  of  the  atmosphere, 
See  art.  56.  This  shews  the  necessity  of  air-holes  to  let 
air  into  the  buckets,  that  the  water  may  have  liberty  to 
get  out  freely. 

Its  disadvantages  are, 

1.  It  loses  the  water  much,  if  it  is  not  kept  close  to 
the  sheeting.     And, 

2.  It  requires  too  great  a  part  of  the  total  fall  to  be 
used  as  head,  which  is  a  loss  of  power,  one  foot  fall 
bejjig  equal  in  power  to  two  feet  head,  by  art.  8. 

Plate  IV.  Fig.  32  is  a  draught,  shewing  the  position 
of  the  shute  for  striking  the  water  on  a  w^heel  in  a  tangent 
direction,  for  all  the  total  perpendicular  descents  from  6 
to  15  feet ;  the  points  of  impact  are  numbered  inside  the 
fig.  with  the  number  of  the  total  fall,  that  each  is  for 
respectively.  The  top  of  the  shute  is  only  about  15  in- 
ches from  the  wheel,  in  order  to  set  the  point  of  impact 
as  high  as  possible,  allowing  .3  feet  above  the  upper  end 
of  the  shute  to  the  top  of  the  water  in  the  penstock,  which 
is  little  enough,  w-hen  the  head  is  often  to  be  run  down 
any  considerable  distance  ;  but  where  the  stream  is  stea- 
dy, being  always  nearly  the  same  height  in  the  penstock, 
2  feet  would  be  sufficient,  especially  in  the  greatest  total 
falls  ;  where  the  quantity  is  less,  raising  the  shute  1  foot 
would  raise  the  point  of  impact  nearly  the  same,  and 
increase  the  power,  because  1  foot  fall  is  equal  in  power 
to  2  feet  head,  by  art.  61. 

On  these  principles,  to  suit  the  applications  of  water, 
as  represented  by  fig.  32,  I  have  calculated  the  following 
table  for  breast  mills.  And,  in  order  that  the  reader 
may  fully  understand  the  principles  on  which  it  is  cal- 
culated, let  him  consider  as  follows  : 

1.  That  all  the  water  above  the  point  of  impact,  called 
head,  acts  wholly  by  percussion,  and  all  below  said  point, 
called  fall,  acts  wholy  by  gravity,  (see  art.  60,)  and  form 
the  2d  and  3d  columns. 

2.  That  half  the  head,  added  to  the  whole  fall,  con- 
stitutes the  virtual  or  effective  descent,  by  art.  61 5  which 
is  the  4th  column. 


168  OF  BREAST  MILLS.  [Chap.  1. 

3.  That  if  the  water  was  permitted  to  descend  freely 
down  the  circular  sheeting,  after  it  passes  the  point  of 
impact,  its  velocity  would  be  accelerated,  by  art.  60,  to 
be,  at  the  lowest  point,  equal  to  the  velocity  of  water 
spouting  from  under  a  head  equal  to  the  whole  descent ; 
therefore  the  maximum  velocity  of  this  wheel  will  be  a 
compound  of  the  velocit)^  to  suit  the  head  and  the  acce- 
leration after  it  passes  the  point  of  impact.  Therefore, 
to  find  the  velocity  of  this  wheel,  I  first  multiply  the 
velocity  of  the  head,  in  column  5,  by  ,577,  (as  for  under- 
shot mills,)  which  gives  the  velocity  suitable  to  the  head ; 
I  then,  (by  the  rule  for  determining  the  velocity  of  over- 
shots,)  say,  as  the  velocity  of  water  descending  21  feet, 
equal  to  37,11  feet  per  second,  is  to  the  velocity  of  the 
wheel  10  feet  per  second,  so  is  the  acceleration  of  velo- 
city, after  it  passes  the  point  of  impact,  to  the  accelerated 
velocity  of  the  wheel ;  and  these  two  velocities  added, 
gives  the  velocity  of  the  wheel  ;  which  is  the  6th  column. 

4.  The  velocity  of  the  wheel  per  second,  multiplied 
by  60,  and  divided  by  the  circumference  of  the  wheel, 
gives  the  revolutions  per  minute ;  7th  column. 

5.  The  number  of  cogs  in  the  cog-wheel,  multiplied 
by  the  number  of  revolutions  of  the  wheel  per  minute, 
and  divided  by  the  rounds  in  the  trundle-head,  will  give 
the  number  of  revolutions  of  the  stone  per  minute  ;  and 
if  we  di^'ide  by  the  number  of  revolutions  the  stone  is 
to  have,  it  gives  the  rounds  in  the  trundle,  and,  when 
fractions  arise,  take  the  nearest  whole  number  ;  columns 
8,  9,  and  10. 

6.  The  cubochs  of  power  required  to  turn  the  stone, 
by  art.  63,  divided  by  the  virtual  descent,  gives  the 
cubic  feet  of  water  required  per  second  ;  column  11. 

7.  The  cubic  feet,  divided  by  the  velocity  of  water 
allowed  in  the  canal,  suppose  1,5  feet  per  second,  gives 
the  area  of  a  section  of  the  canal ;  column  12. 

8.  If  the  mill  is  to  be  double  geared,  take  the  revolu- 
tions of  the  wheel  from  column  7  of  this  table,  and  look 
in  column  4  of  the  undershot  table,  art.  70,  for  the  num- 
ber of  revolutions  nearest  to  it,  and  against  that  number 
you  have  the  gears  that  will  give  a  5  feet  stone  the  right 
motion. 


Chap.  1.] 


OF  BREAST  MILLS. 


169 


THE  MILL- WRIGHT'S  TABLE 


BREAST  MILLS, 

Calculated  for  a  Water-wluel  fifteen  Feet,  and  Stones  five  Feet,  diameter; 
the  Water  being  shot  on  in  a  tangent  direction  to  the  circutpferencc  of 
ihc  Wheel. 


-a  2 


o  :;. 
c  ft 


>2  3 

3 


feet,  feet    fee' 


4,5 

5, 

5,5 

5.9 

6,2 

6  5 

6,8 

6.8 

6,9 


1,5 

2, 

25 

3,1 

3,8 

4,5 

5,3 

6,2 

7,1 


feet. 


feet 


5,75  17,13 
4,5    18, 
5,25|18.99 
6,05ll9,48 
6,9  '20,16 


feet. 


No. 


7,75 
8,7 
9.6 
10,55 
11,5 


20,64 

21,11 

21.11 

21,3 

21,13 


No. 


10,61  13.5 
11,3    14,4 
12,07  15,3 
12,5316, 
13,0716,6 
13,5317, 
14,03  17.81 
14,35  18,28 
14,4118.35 
14  7618,56 


112 
112 
104 


^ 

s- 

o 

n 

(T 

n 

n 

3 

H- 

» 

tn 

*• 

» 

n 

J-   ^. 

O 

•^ 

# 

T) 

n 

Ct! 

en 

g^ 

n 

IT* 

N.'  No.  cub.  ft.|  su.  ft. 


15100,8 
16 100,8 
16   99,41 
104;i6'l02,7 
9616;  99,6 
96|l6l02, 


9617 
9618 
96|l8 
96118 


6   I     7   \    8  19 


100,5 
97,5 
97,8 
98,4 


29,8  I 
24,83 
21,29 
18,45 
16,2 
14,42 
12,73 
11,63 
10,59 
9,72 


10         11 


19.25 

16,55 

14,19 

12,3 

10,8 

9,61 

8,49 

7,75 

7,06 

6,48 

12 


170  OF  BREAST  MILLS.  [Chap.  1 


Use  of  the  Table  for  Breast  Mills. 

Having  a  seat  with  above  6  feet  fall,  but  not  enough 
for  an  overshot  mill,  and  the  water  being  scarce,  so  that 
you  wish  to  make  the  best  use  of  it,  leads  you  to  the 
choice  of  a  breast  mill. 

Cast  off  about  1  foot  for  fall  in  the  tail  race  below  the 
bottom  of  the  wheel,  if  much  subject  to  back-water ;  and 
suppose  you  have  then  9  feet  total  descent;  look  for  it 
in  the  first  column  of  the  table,  and  against  it  you  have 
it  divided  into  5,9  feet  head  above,  and  3,1  feet  fall  be- 
low the  point  of  impact,  which  is  the  highest  point  that 
the  water  can  be  fairly  struck  on  the  A^'heel,  leading  the 
head  3  feet  deep  above  the  shute  ;  which  is  equal  to 
6,5  feet  virtual  or  effective  descent ;  the  velocity  of  the 
water  striking  the  wheel  18,99  feet,  velocity  of  the  wheel 
12,07  feet  per  second,  will  revolve  16  times  in  a  minute  ; 
and,  if  single  geared,  104  cogs,  and  16  rounds,  gives  the 
stone  99,4  revolutions  in  a  minute,  requires  21,29  cubic 
feet  of  water  per  second;  the  area  of  a  section  of  the 
canal  must  be  14,19  feet,  about  3  feet  deep,  and  5  feet 
wide.  If  the  stones  be  of  any  other  size,  it  is  easy  to 
proportion  the  gears  to  give  them  any  number  of  revo- 
lutions required. 

If  you  wish  to  proportion  the  size  of  the  stones  to  the 
power  of  your  seat,  multiply  the  cubic  feet  of  water  your 
stream  affords  per  second,  by  the  virtual  descent  in 
column  4,  and  that  product  is  the  power  in  cubochs ; 
then  look  in  the  table,  in  art.  63,  for  the  size  of  the  stone 
that  nearest  suits  that  power. 

For  instance,  suppose  your  stream  affords  ji  cubic 
feet  of  water  per  second,  then  14  multiplied  by  6,05 
feet  virtual  descent,  produces  84,7  cubochs  of  power  ; 
which,  in  the  table  in  art.  63,  comes  nearest  to  4,5  feet 
for  the  diameter  of  the  stones  ;  but,  by  the  rules  laid 
down  in  art.  63,  the  size  may  be  found  more  exactly. 

Note,  6  cubochs  of  power  are  required  to  every  super 
ficial  foot  of  the  stones. 


Chap.  1.]  OF  OVERSHOT  MILLS.  171 

ART.    73. 

OF  OVERSHOT  MILLS. 

Fig.  33,  plate  IV,  is  an  overshot  wheel ;  the  water  is 
laid  on  at  the  top,  so  that  the  upper  part  of  the  column 
will  be  in  a  true  tangent  direction  with  the  circumference 
of  the  wheel,  but  so  that  all  the  water  may  strike  within 
the  circle  of  the  wheel. 

The  gate  is  drawn  about  30  inches  behind  the  perpen- 
dicular line  from  the  centre  of  the  wheel,  and  the  point 
of  the  shute  ends  at  said  perpendicular,  with  a  direction 
a  little  downwards,  which  gives  the  water  a  little  velocity 
downwards  to  follow  the  wheel ;  for  if  it  be  directed 
horizontally,  the  head  will  give  it  no  velocity  down- 
wards and  if  the  head  be  great,  the  parabolic  curve, 
which  the  spouting  water  forms,  will  extend  beyond  the 
outside  of  the  circle  of  the  wheel,  and  it  will  incline  to 
fly  over.     See  art.  44  and  60. 

The  head  above  the  wheel  acts  by  percussion,  as  on 
an  undershot  wheel,  and  we  have  shewn,  art.  43,  that 
the  head  should  be  such  as  to  give  the  water  velocity  3 
for  2  of  the  wheel.  After  the  water  strikes  the  wheel 
it  acts  by  gravity ;  therefore,  to  calculate  the  power,  we 
must  take  half  the  head  and  add  it  to  the  fall,  for  the 
virtual  descent,  as  in  breast  mills. 

The  velocity  of  overshot  wheels  is  as  the  square  roots 
of  their  diameters.     See  art.  43. 

On  these  principles,  I  have  calculated  the  following- 
table  for  overshot  wheels ;  and,  in  order  that  the  reader 
may  understand  it  fully,  let  him  consider  well  the  follow- 
ing premises  : 

'1 .  That  the  velocity  of  the  water  spouting  on  the  wheel 
must  be  one  and  a  half  the  velocity  of  the  wheel,  by  art. 
43  :  then,  to  find  the  head  that  will  give  said  velocity, 
say,  as  the  square  of  16,2  feet  per  second,  is  to  4ieet, 
the  head  that  gives  that  velocity,  so  is  the  square  of  the 
velocity  required,  to  the  head  that  will  give  that  velocity : 
but  to  this  head,  so  found,  we  must  add  a  little  by  con- 
jecture, to  overcome  the  friction  of  the  aperture.  See 
art.  55. 


172  OF  OVERSHOT  MILLS.  [Chap.  1 

In  this  table,  I  have  added  to  the  heads  of  wheels 
from  9  to  12  feet  diameter  ,1  of  a  foot,  and  from  IS  to 
20  I  have  added  1  tenth  more,  for  every  foot  increase 
of  diameter,  and  from  20  to  30  feet  I  have  added  ,05 
more  to  every  foot  diameter's  increase  ;  which  gives  a 
30  feet  wheel  1,5  feet  additional  head,  while  a  nine  feet 
wheel  has  only,  1  tenth  of  a  foot,  to  overcome  the  fric- 
tion. The  reason  of  this  great  difference  will  appear 
when  we  consider  that  the  friction  increases  as  the  aper- 
ture decreases,  and  as  the  velocity  increases  :  but  this 
much  depends  on  the  form  of  the  gate,  for  if  that  be 
nearly  square,  there  will  be  but  little  friction,  but  if  very 
oblong,  say  24  inches  by  half  an  inch,  then  it  will  be 
very  great. 

The  heads,  thus  found,  compose  the  3d  column. 

2.  The  head,  added  to  the  diameter  of  the  wheel, 
makes  the  total  descent,  as  is  column  1. 

3.  The  velocity  of  the  wheel  per  second,  taken  from 
the  table  in  art.  43,  and  multiplied  by  60,  and  divided  by 
the  circumference  of  the  wheel,  quotes  the  number  of 
revolutions  of  the  wheel  per  minute,  and  is  column  4. 

4.  The  number  of  revolutions  of  the  wheel  per  minute, 
multiplied  by  the  number  of  cogs  in  all  the  driving 
wheels  successively,  and  that  product  divided  by  the 
product  of  all  the  leading  wheels,  qiiotes  the  number  of 
revolutions  of  the  stone  per  minute,  and  is  column  9, 
double  gear,  for  5  feet  stones  ;  and  column  12,  single 
gear,  for  6  feet  stones. 

5.  The  cubochs  of  ])ower  required  to  drive  the  stone, 
by  table  in  art.  63,  divided  by  the  virtual  or  effective 
descent,  which  is  half  the  head  added  to  the  (foil  or) 
diameter  of  the  wheel,  quotes  the  cubic  feet  of  Avater 
required  per  second  to  drive  the  stone,  and  is  column  13. 

6.  The  cubic  feet  required,  divided  by  the  velocity 
you  intend  the  water  to  have  in  the  canal,  quotes  the 
area  c^  a  section  of  the  canal.  The  width  multiplied  by 
the  depth,  must  always  produce  this  area.     See  art.  64. 

7.  The  number  of  cogs  in  the  wheel,  multiplied  by 
the  quarter  inches  in  the  pitch,  produces  the  circumfe- 
rence of  the  pitch  circle :  which,  multiplied  by  7,  and 


Chap.  1.]         OF  OVERSHOT  MILLS.  173 

divided  by  23,  quotes  the  diameter  in  quarter  inches ; 
which,  reduced  to  feet  and  parts,  is  column  15.  The 
reader  may  here  at  once  observe  how  near  the  cog- 
wheel, in  the  single  gear,  will  be  to  the  water ;  that  is, 
how  near  it  is,  in  size,  equal  to  the  water-wheel. 

Use  of  the   Table. 

Having  with  care  levelled  the  seat  on  which  you  mean 
to  build,  and  found,  that  after  deducting  1  foot  for  fall 
below  the  wheel,  and  a  sufficiency  for  the  sinking  of  the 
head  race,  according  to  its  length  and  size,  and  having  a 
total  descent  remaining  sufficient  for  an  overshot  wheel, 
suppose  17  feet ;  then  look  in  column  1  of  the  table,  for 
the  descent  nearest  to  it,  we  find  16,74  feet,  and  against 
it  a  wheel  14  feet  diameter;  head  above  the  wheel  2.7 
feet;  revolutions  of  the  wheel  per  minute  11,17  ;  (and 
double  gears,  to  give  a  5  feet  stone  98,7  revolutions  per 
minute  ;  also,  single  gears,  to  give  a  6  feet  stone  76,6 
revolutions  per  minute  ;)  the  cubic  feet  of  water  required 
for  a  5  feet  stone  7,2  feet  per  second,  and  the  area  of  a 
section  of  the  canal  5  feet,  about  2  feet  deep,  and  2,5 
feet  wide. 

If  you  choose  to  proportion  the  size  of  the  stones  ex- 
actly to  suit  the  power  of  the  seat,  do  it  as  directed  in  art. 
63.  All  the  rest  can  be  proportioned  by  the  rules  by 
which  the  table  is  calculated. 


174 


OF  OVERSHOT  MILLS. 


[Chap. 


THE  MILLWRIGHT'S  TABLE 


OVERSHOT  MILLS, 


CALCULATED   FOU   FIVE  FEET    STONES,  DOUBLE  GEAR,  AND  SIX 
FEET  STONES,  SINGLE  GEAR. 


H 

I 

5! 

Double  gear,  5 

Single  gear, 

0 

> 

0 

~>S.  p 

r»    CO     — 

;   r.  P 

c 

3 

tr 
re 

feet  stones, 
r— -- ^ , 

6  ft.  stones. 

5^ 
0' 

0  re  »■ 

=•  n  P 

0^  3 

sr^   re 

***    fii    m 

.,   0   =■ 

■z, 

0 

5C 

fc 

fT' 

■0  re      ■ 

re   fi  c* 
(o   ^  re 

:scent  of  the  water,  w  hi 
ible  made  to  suit  the  d 
wheel  and  head  above  i 

C 

?! 

n 

—. 

C_ 

re 

s= 

zr 
re 
re 

3ve  the  wheel,  allowing 
n  of  the  aperture,  so  as 
t(-r  velocity  3  for  2  of  the 

re 
< 
0 

3  e 
3  5- 

S.    3 

re  » 

■    0 

re 

p 
0 

re 

0 

0!) 
CO 

5' 

3 

p 

1 

0 

re 

p 
0 

3 

re 

0 

0 

3 

re 
1 
0 
0 

J!? 

0 

c 
3 

5' 

=r 
re 

3 

a. 

re 
o_ 
c" 

0' 

3 
%% 

0) 

0 

re 

*^ 

5' 

re 
0 

0 

k 

3- 

re 

3 
3- 

re 
< 

c' 

5 

3 

7  re 

W) 

0 
re 

^  0 
re  ;^ 

5 ;? 

re  B, 
re 

ii  seciion  of  the  canal,  a 
locity  ot  tlie  water  in  it 
er  second. 

•      3-1 

re   - 

CO    "Z. 
ce    _. 

5"o 

gt;  3- 
fT  2. 

3Z 
"5.7 

ch  is  i 
iamete 

it. 

?  0  o" 
re  <  ET 

n 
re 

•a 

sr 
re 
2. 

re 

re 
re 

re 

•a 

re 
3 

re 

re" 

re 

3 

re 
0 

0 

0  c" 
re   3 

"^  = 

.""  re  re 

-1 

21 

44 

16 

102,9 

60 

11 

78, 

-"" 

h-!rq 

*.  %■ 

feet. 

ft. 

feet. 

54 

cn.ft. 

Slip,  ft 

feet,  inches. 

10,51 

9 

1,51 

14,3 

11,46 

11,46 

6:9  0-4  12  22 

11,74 

10 

1,74 

13, 

54 

21 

48 

18 

98, 

60 

10 

78, 

10,3 

10,3 

12,94 

11 

1,94 

12,6 

60 

21 

48 

18 

96, 

66 

11 

75,6 

9,34 

9,34 

7:5  1-4 

14,2 

12 

2,2 

12, 

66 

23 

48 

17 

97, 

66 

10 

79,2 

8,53 

8,53 

15,47 

13 

2,47 

11,54 

66 

21 

48 

17 

99,3 

84 

12 

80,7 

7,92 

7,92 

9:5  1-2 

16.74 

K 

2.74 

11,17 

72 

23 

48 

17 

98,7 

96 

14 

76,6 

7.2 

7,2 

10:9  3-4    6-22 

17,99 

15 

2,99 

10,78 

78 

23 

48 

18 

98,3 

96 

13' 

81.9 

6,77 

6,77 

19,28 

16 

3,28 

10,4 

78 

23 

48 

17 

99,5 

120 

16 

76, 

6,4 

6,4 

13:6  1.4    2-22 

20,5 

17 

3,5 

10,1 

78 

21 

48 

18 

96,6 

120 

15 

80,8 

6, 

6. 

21,8 

18 

3.8 

9,8 

84 

24 

48 

17 

97. 

128 

16 

78,4 

5,56 

5,56 

14:5  0-4    8-22 

23,03 

19 

4,03 

9,54 

84 

23 

48 

17 

98,3 

128 

15 

81,4 

5,32 

5.32 

24,34 

20 

4,34 

9,3 

88 

2^. 

48 

17 

100, 

128 

15 

79.3 

5,04 

5,04 

25,54 

21 

4.54 

9,1 

88 

23 

48 

17 

98,3 

128 

15 

77,6 

4,81 

4,81 

26,86 

22 

4.86 

8,9 

96 

24 

48 

17 

100.5 

128 

14 

81,4 

4,57 

4,57 

27,99  2] 

4,99 

8,7 

96 

25 

54 

18 

100,2 

4,34 

4,34 

29,27  24 

5,27 

8,5 

96 

25 

54 

17 

103, 

4,19 

4,19 

30,45j25 

5,4.1 

8,3 

96 

25  54 

17 

101, 

4, 

4, 

31,57|26 

5,57 

8,19 

96 

25'54 

17 

99,6 

3,82 

3,82 

32.77I27 

5,77 

8,03 

104 

25;54 

18 

100,2 

3,7 

^,7  i 

33,96;28 

5.96 

7,93 

104 

?.5  54 

18 

99, 

3,6 

3.6  1 

3.5,15:29 

6,15 

7,75 

112 

2654 

18 

100.1 

3,4 

3.4  i 

36,4   30 

6,4 

7,6.S 
4 

5 

2654 

18 
8 

98,6 

3,36 

3,36 

1      I2 

'    3 

6 

7 

9 

10 

11 

12 

13 

14     i 

15 

Chap.!.]  OF  OVERSHOT  MILLS.  ITS 


Observations  oji  the  Table. 

1.  It  appears,  that  single  gear  does  not  much  suit  this 
construction  ;  because,  where  the  water-wheels  are  low, 
their  motion  is  so  slow  that  the  cog-wheels,  (if  made  large 
enough  to  give  sufficient  motion  to  the  stone,  without 
having  the  trundle  too  small,  see  art.  23,)  will  touch  the 
water :  And  again,  when  the  w^ater-wheels  are  high, 
above  20  feet,  the  cog-wheels  require  to  be  so  high,  in 
order  to  give  motion  to  the  stone  without  having  the 
trundle  too  small,  that  they  become  unwieldy,  and  the 
husk  too  high,  spindle  short,  he.  so  as  to  be  inconvenient. 
Therefore,  "single  gear  seems  to  suit  overshots  only  where 
the  diameter  of  the  water-wheel  is  between  12  and  18 
feet;  and  even  with  them  the  water-wheel  will  have  to 
run  rather  too  fast,  or  the  trundle  be  rather  too  small, 
and  the  stones  should  be  6  feet  diameter  at  least. 

2.  I  have,  in  the  preceding  tables,  allowed  the  water 
to  pass  along  the  canal  with  1,5  feet  per  second  velocity; 
but  have  since  concluded  that  1  foot  per  second  is  nearer 
the  proper  motion ;  that  is,  about  20  yards  per  minute ; 
then  the  cubic  feet  required  per  second,  will  be  the  area 
of  a  section  of  the  canal,  as  in  column  14  of  this  table. 

3.  Although  I  have  calculated  this  table  for  the  velo- 
cities of  the  wheels  to  vary  as  the  square  roots  of  their 
diameters,  which  makes  a  30  feet  wheel  move  11,99  feet 
per  second,  and  a  twelve  feet  wheel  to  move  7,57  feet  per 
second;  yet  they  will  do  to  have  equal  velocity,  and 
head,  which  is  the  common  practice  among  mill-wrights. 
But,  for  the  reasons  I  have  mentioned  in  art.  43,  I  prefer 
giving  them  the  velocity  and  head  assigned  in  the  table, 
in  order  to  obtain  steady  motion. 

4.  Many  have  been  deceived,  by  observing  the  ex- 
ceeding slow  and  steady  motion  of  some  very  high  over- 
shot wheels  working  forge  or  furnace  bellows,  conclud- 
ing therefrom,  that  they  will  work  equally  steady  with  a 
very  slow  as  with  any  quicker  motion,  not  considering, 
perhaps,  that  it  is  the  principle  of  the  belloU's  that  regu- 
lates the  motion  of  the  wheel,  which  is  different  from  any 


176  OF  OVERSHOT  MILLS.  [Chap.l. 

other  resistance,  for  it  soon  becomes  perfectly  equable ; 
therefore  the  motion  will  be  uniform,  which  is  not  the 
case  with  any  kind  of  mills. 

5.  Many  are  of  opinion,  that  water  is  not  well  applied 
by  an  overshot  wheel;  because,  say  they,  those  buckets 
near  above  or  below  the  centre,  act  on  too  short  a  lever. 
In  endeavouring  to  correct  this  error,  I  have  divided  the 
fall  of  the  overshot  wheel,  fig-  33,  plate  IV,  into  feet,  by 
dotted  lines.  Now,  by  art.  53  and  54,  every  cubic  foot 
of  water  on  the  wheel  produces  an  equal  quantity  of 
power  in  descending  each  foot  perpendicular,  called  a 
cuboch  of  pouer;  because,  where  the  lever  is  shortest, 
there  is  the  greatest  quantity  of  water  within  the  foot  per- 
pendicular; or,  in  other  words,  each  cubic  foot  of  water 
is  a  much  longer  time,  and  passes  a  gi'eater  distance,  in 
descending  a  foot  perpendicular,  than  where  it  is  long- 
est; which  exactly  compensates  for  the  deficiency  in  the 
length  of  lever.  And,  considering  that  the  upper  and 
lower  parts  of  the  wheel  do  not  run  away  from  the 
gravity  of  the  water,  so  much  as  the  breast  of  the  wheel, 
we  must  conclude,  that  the  upper  and  lower  feet  of  per- 
pendicular descent  (in  theory)  actually  produce  more 
power  than  the  middle  two  feet;  but  (in  practice)  the 
lower  foot  is  entirely  lost,  by  the  spilling  of  the  water 
out  of  the  buckets.     See  this  demonstrated,  art.  54.* 

Of  Mills  moved  by  Re-action. 

We  have  now  treated  of  the  four  different  kinds  of 
mills  that  are  in  general  use.  There  are  others,  the  in- 
vention, or  improvements  of  the  late  ingenious  James 
Rumsey,  which  move  by  the  re-action  of  the  water.  One 

•  The  Messrs.  EUicoHs  have  coiistructeil  overshot  wheels  at  their  mills 
wear  Baltimore,  so  that  they  retain  the  water  the  whole  of  its  descent,  de- 
livering- it  under  the  centre  ol  the  wheel.  This  is  done  by  iialtsoaling  the 
wheel  outside  of  the  rim,  and  to  prevent  the  water  from  splashing  over 
the  sides  as  it  conges  on  the  wheel,  they  extend  the  rim  outside  of  the  buck- 
ets by  nailing  ro  ind  it  two  pieces  one  and  a  iialf  inch  thick,  on  each  ritn, 
increasing  the  diameter  three  inches ;  these  also  help  to  hold  in  the  buckets 
and  soaling  firmly.  Two  advantages  are  expected  from  this  construction; 
first,  retaining  tlie  water  the  whole  of  the  descent ;  secondly,  the  wheel 
wdl  run  more  steadily,  as  it  cannot  fly  off  as  rapidly  when  the  resistance  is 
taken  ofl",  as  it  would  have  left  the  water  on  the  rising  side. 


Chap.  1.]  OF  MILLS  MOVED  BY  RE-ACTION.     177 

of  these  is  said  to  do  well  where  there  is  much  back- 
water ;  it  being  small,  and  of  a  true  circular  form,  the 
back-water  does  not  resist  it  much.  I  shall  say  but  little 
of  these,  supposing  the  proprietors  mean  to  treat  of  them ; 
but  may  say,  that  there  appears  to  me  but  two  principles 
by  which  water  can  be  applied  to  move  mill-wheels,  viz. 
Percussion  and  Gravity. 

For  the  different  effects  of  equal  quantities  of  water, 
with  equal  perpendicular  descents,  applied  by  these  dif- 
ferent principles,  see  art.  8  and  68. 

Water  may  be  applied,  by  percussion,  two  ways,  viz. 
by  action  (which  is  when  it  strikes  the  floats  of  a  wheel) 
and  by  re-action,  which  is  when  it  issues  from  within  the 
wheel,  and,  by  its  re-action,  moves  it  round ;  and  these 
two  are  equal,  by  3d  general  law  of  motion,  art.  7. 

For  the  effects  of  centrifugal  force,  and  the  inertia  of 
the  water,  on  this  application  of  re-action,  see  axioms  I, 
and  II,  art.  1 ;  and  art.  13.  The  principle  of  inertia  will 
operate  in  proportion  to  the  quantity  of  water  used ; 
therefore  this  application  will  suit  high  heads  better  than 
low  ones. 

Water  may  be  applied,  by  gravity,  two  ways,  viz. 
either  by  spouting  it  high  on  the  wheel,  into  tight  buck- 
ets, as  on  common  overshots,  or  by  causing  the  whole 
head  of  water  to  press  on  the  floats,  at  the  lower  side  of 
the  wheel,  which  is  so  constructed  that  the  water  cannot 
escape,  but  as  the  wheel  moves,  and  at  the  same  time 
keeping  clear  of  the  paradoxical  principle  mentioned  in 
arts.  48  and  59  ;  w^hich  cannot  be  done  unless  the  floats 
are  made  to  move  on  pivots,  so  as  to  fold  in  on  one  side 
of  the  wheel,  and  open  out,  to  receive  the  weight  of  the 
water,  on  the  other.  And  these  two  applications  are 
equal  in  theory,  as  will  appear  plain  by  art.  54,  plate  III. 
fig.  20 ;  yet  they  may  differ  greatly  in  practice.* 

•  In  the  year  1786,  I  invented  and  made  a  model  of  a  wheel  of  this  struc  • 
ture,  intending  thereby  to  apply  steam  to  propel  land-carriages,  and  exhi- 
bited a  drawing  thereof  to  the  legislature  of  Maryland,  and  obtained  a 
patent  (for  my  improvements  in  mills,  and  also)  for  applying  steam  to 
land-carriages,  in  that  state;  but  coald  not  attend  to  put  it  iii  practice. 
Since  which  time,  the  late  ingenions  James  Rumsey  has  applied  this  wheel 
to  water-mills,  which  I  did  not  intend  to  do.  This  may  properlv  be  crdlcd 
the  Valve  Wheel.  .   i     i      . 


178  RULES  AND  CALCULATIONS.   [Chap.  2. 


CHAPTER  IL 

ART.    74. 
RULES  AND  CALCULATIONS. 

THE  fundamental  principle,  on  which  is  founded  all 
rules  for  calculating  the  motion  of  wheels,  produced  by 
a  combination  of  wheels,  and  for  calculating  the  number 
of  cogs  to  be  put  in  wheels,  to  produce  any  motion  that 
is  re(]uired,  see  in  art.  20 ;  \^'hich  is  as  follows  : 

If  the  revolutions  that  the  first  moving  wheel  makes 
in  a  minute  be  multiplied  by  the  number  of  cogs  in  all 
the  driving  wheels  successively,  and  the  product  noted  ; 
and  the  revolutions  of  the  last  leading  wheel  be  multi- 
plied by  the  number  of  cogs  in  all  the  leading  wheels 
successively,  and  the  product  noted ;  these  products 
will  be  equal  in  all  possible  cases.  Hence  \^e  deduce 
the  following  simple  rules  : 

1st.  For  finding  the  motion  of  the  mill-stone :  the 
revolutions  of  the  water-wheel,  and  cogs  in  the  wheels, 
being  given, 

RULE. 

Multiply  the  revolutions  of  the  v\^ater-wheel  per  mi- 
nute, by  the  number  of  cogs  in  all  the  driving  v\heels 
successively,  and  note  the  product;  and  multiply  the 
number  of  cogs  or  rounds  in  all  the  leading  wheels  suc- 
cessively, and  note  the  product;  then  divide  the  first 
product  by  the  last,  and  the  quotient  is  the  number  of 
revolutions  of  the  stone  per  minute. 

EXAMPLE. 

Given,  the  revolutions  of  the  water-uheel 

per  minute,         ------       10,4 

No.  of  cogs  in  the  master  cog-wheel  78  7  D^Typj.,, 

No.  of  do.  in  the  counter  cog-wheel         48  3 


Chap.  2.]      RULES  AND  CALCULATIONS.  ir9 

No.  of  rounds  in  the  vvallower         -         ^^  ?  t      a 
No.  of    do.     in  the  trundle  -  ^ ^  ^  1-eaders. 

Then  10,4,  the  revolutions  of  the  water-wheel,  multi- 
plied by  78,  the  cogs  in  the  master  wheel,  and  48,  the 
cojTs  in  the  counter  wheel,  is  equal  to  38937,6;  and  23 
rounds  in  the  wallower,  multiplied  by  17  rounds  in  the 
trundle,  is  equal  to  391,  by  which  we  divide  38937,6, 
and  it  quotes  99,5,  the  revolutions  of  the  stone  per  mi- 
nute; which  are  the  calculations  for  a  16  feet  wheel,  in 
the  overshot  table. 

2d.  For  finding  the  number  of  cogs  to  be  put  in  the 
wheels,  to  produce  any  number  of  revolutions  required 
to  the  mill-stone,  or  any  wheel, 

RULE. 

Take  any  suitable  number  of  cogs  for  all  the  wheels, 
except  one;  then  multiply  the  revolutions  of  the  first 
mover  per  minute,  by  all  the  drivers,  except  the  one 
wanting  (if  it  be  a  driver)  and  the  revolutions  of  the 
wheel  required,  by  all  the  leaders,  and  divide  the  great- 
est product  by  the  least,  and  it  will  quote  the  number  of 
co,^s  required  in  the  w  heel  to  produce  the  desired  revo- 
lutions. 

Note,  if  any  of  the  wheels  be  for  straps,  take  their 
diameter  in  inches  and  parts,  and  multiply  and  divide 
with  them,  as  with  the  cogs. 

EXAxMPLE. 

Given,  the  revolutions  of  the  water-wheel 
And  we  choose  cogs  in  master  wheel  78 
Ditto  in  the  counter  wheel  -  48 

And  rounds  in  the  wallower        -  23 

The  number  of  the  trundle  is  required,  to  give  the 
stone  99  revolutions. 

Then  10,4  multiplied  by  78,  and  48,  is  equal  to  38937,6; 
and  99,  muhiplied  by  23,  is  equal  to  2277,  bv  which 
divide  38937,6,  and  it  quotes  16,66;  instead  of  which, 
I  take  the  nearest  whole  number,  17,  for  the  rounds  in 
the  trundle,  and  find,  by  rule  1st,  that  it  produces  99,5 
revolutions,  as  required. 


180         RULES  AND  CALCULATIONS.         [Chap.  2. 

For  the  exercise  of  the  learner,  I  have  constructed 
fig.  7,  plate  XI;  which  I  call  a  circle  of  motion,  and 
which  serves  to  prove  the  fundamental  principle  on 
which  the  rules  are  founded ;  the  first  shaft  being  also 
the  last  of  the  circle. 

A  is  a  cog-wheel  of  SO  cogs,  and  is  a  driver. 


B 

do. 

24 

leader. 

C 

do. 

24. 

driver. 

D 

do. 

30 

leader. 

E 

do. 

25 

driver. 

F 

do. 

30 

leader. 

G 

do. 

36 

driver. 

H 

do. 

20 

leader. 

But  if  we  trace  the  circle  the  backward  way,  the  lead- 
ers become  drivers. 

I  is  a  strap-wheel  14|  inches  diameter,  driver. 
K  do.  30     do.  -  leader. 

L       cog-wheel      12  cogs,  -  driver. 

M  do.  29    do.  -  leader. 

MOTION  OF  THE  SHAFTS. 

The  upright  shaft,  and  first  driver,  AH  36  revs,  in  a  min. 

BC  30  do. 
DE24do. 
FG20do. 
HA  36  do. 
M  4  do.  which  is 
the  shaft  of  a  hopperbo}'. 

If  this  circle  be  not  so  formed,  as  to  give  the  first  and 
last  shafts  (which  are  here  the  same)  exactly  the  same 
motion,  one  of  the  shafts  must  break  as  soon  as  they  are 
put  in  motion. 

The  learner  may  exercise  the  rules  on  this  circle,  un- 
til he  can  form  a  similar  circle  of  his  own;  and  then  he 
need  never  be  afraid  to  undertake  to  calculate  any  motion, 
&c.  afterwards. 

-  I  omit  shewing  the  vrork  for  finding  the  motion  of  the 
several  shafts  in  this  circle,  and  the  wheels  to  produce 


Chap.  2.]  RULES  AND  CALCULATIONS.  181 

said  motion  ;  but  leave  it  for  the  learner  to  practise  the 
rules  on. 

EXAMPLES. 

1st.  Given,  the  first  mover  AH  36  revolutions  per 
minute,  and  first  driver  A  20  cogs,  leader  B  24;  required, 
the  revolutions  of  shaft  BC.  Answer,  30  revolutions  per 
minute. 

2d.  Given,  first  mover  36  revolutions  per  minute, 
drivers  20 — 24 — 25,  and  leaders  24 — 30 — 30  ;  required, 
the  revolutions  of  the  last  leader.  Answer,  20  revolu- 
tions per  minute. 

3d.  Given,  first  mover  20  revolutions  per  minute,  and 
first  driver,  strap-wheel,  14^  inches,  cog-wheel  IS,  and 
leader,  strap-wheel,  30  inches,  cog-wheel  29;  required, 
the  revolutions  of  the  last  leader,  or  last  shaft.  Answer, 
4)  revolutions. 

4th.  Given,  first  mover  36  revolutions,  driver  A  20, 
C  2%  leader  B  24,  D  30  ;  required,  the  number  of 
leader  F,  to  produce  20  revolutions  per  minute.  Answer, 
30  cogs. 

5th.  Given,  first  mover  36  revolutions  per  minute, 
driver  A  20,  C  24,  E  25,  driver  pulley  14|  inches  dia- 
meter, L  12,  and  leader  B  24,  D  30,  F  30,  M  29  ;  re- 
quired, the  diameter  of  strap-wheel  K,  to  give  shaft  4 
four  revolutions  per  minute.  Answer,  30  inches  dia- 
meter. 

The  learner  may,  for  exercise,  work  the  above  ques- 
tions, and  e^•ery  other  that  he  can  propose  on  the  circle. 


ART.    75. 


Mathematicians  have  laid  down  the  following  propor- 
tions for  finding  the  circumference  of  a  circle  by  its  dia- 
meter, or  the  diameter  by  the  circumference  given,  viz. 

As  1  is  to  3,1416,  so  is  the  diameter  to  the  circumfe- 
rence ;  and  as  3,1416  is  to  1,  so  is  the  circumference  to 
the  diameter  :  Or,  as  7  is  to  22,  so  is  the  diameter  to  the 
circumference  ;  and  as  22  is  to  7,  so  is  the  circumference 


182  RULES  AND  CALCULATIONS.  [Chap.  2. 

to  the  diameter.  The  last  proportion  makes  the  diameter 
a  little  the  largest ;  therefore  it  suits  mill-vvrights  best 
for  finding  the  pitch  circle  ;  because  the  sum  of  the  dis- 
tances, from  centre  to  centre,  of  all  the  cogs  in  a  wheel, 
makes  the  circle  too  short,  especially  where  the  number 
of  cogs  are  few,  because  the  distance  is  taken  in  straight 
lines,  instead  of  the  circle.  In  a  wheel  of  6  cogs  only, 
the  circle  will  be  so  much  too  short,  as  to  give  the  dia- 
meter -jI^  parts  of  the  pitch  or  distance  of  the  cogs  too 
short.     Hence  we  deduce  the  following 

RULES  FOR  FINDING  THE  PH  CH  CIRCLE. 

Multiply  the  number  of  cogs  in  the  wheel,  by  the 
quarter  inches  in  the  pitch,  and  that  product  by  7,  and 
divide  by  23,  and  the  quotient  is  the  diameter  in  quarter 
inches,  which  is  to  be  reduced  to  feet. 

EXAMPLE. 

Given,  84  cogs  4)|  inches  pitch ;  required,  the  diameter 
of  the  pitch  circle. 

Then,  by  the  rule,  84<  multiplied  by  18  and  7i  is  equal 
to  10584;  which,  divided  by  22,  is  equal  to  "^81^%  quar- 
ter inches,  equal  to  10  feet  ^^~JL  inches,  for  the  diameter 
of  the  pitch  circle  required. 


ART.    7Q. 

A  true,  simple,  and  expeditious  method  of  finding  the 
diameter  of  the  pitch  circle,  is  to  find  it  in  measures  of 
the  pitch  itself  that  you  use. 

RULE. 

Multiply  the  number  of  cogs  by  7,  and  divide  by  22, 
and  you  have  the  diameter  of  the  pitch  circle,  in  mea- 
sures of  the  pitch,  and  S2  parts  of  said  pitch. 

EXAMPLE. 

Given,  7^  cogs  ;  required,  the  diameter  of  the  pitch 
circle.     Then,  by  the  rule, 


Chap.  2.]      RULES   AND  CALCULATIONS.         183 

78 

7 


22)546(24||  C  Measures  of  tlie  pitch  for  the  diame- 
44  I      ter  of  the  'circle  required. 

106 
88 

18 

Half  of  which  diameter.  IS/^of  the  pitch,  is  the  radi- 
us, or  half  diameter,  by  which  the  circle  is  to  be  swept. 

To  use  this  rule,  set  a  pair  of  compasses  to  the  pitch, 
and  screM'  them  fast,  not  to  be  altered  until  the  wheel  is 
pitched  ;  divide  the  pitch  into  22  equal  parts  ;  then  step 
12  steps  on  a  straight  line  with  the  pitch  compasses,  and 
9  of  these  equal  parts  of  the  pitch  makes  the  radius  that 
is  to  describe  the  circle. 

To  save  the  trouble  of  dividing  the  pitch  for  every 
wheel,  the  workman  may  mark  the  different  pitch,  which 
he  commonly  uses,  on  the  edge  of  his  two  foot  rule  (or 
make  a  little  rule  for  the  purpose)  and  carefully  divide 
them  there,  where  they  will  be  always  ready  for  use. 
See  plate  IV,  fig.  35. 

By  these  rules,  I  have  calculated  the  following  table 
of  the  radiuses  of  pitch  circles  of  the  different  wheels 
commonly  used,  from  6  to  136  cogs. 


184        RULES  AND  CALCULATIONS.       [Chap.  2. 


A  TABLE 

OF  THE 

PITCH  CIRCLES  OF  THE  COGWHEELS 

COMMONLY  USED, 

From  6  to  136  cogfs,  both  in  measures  of  the  Pitch,  and  in  feet,  inches, 
and  parts. 


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pitch   circl 
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10,2 

3   :   2:   14 

36 

5  16 

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20,5 

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6     41-2 

2:    2:1:10  1.2 

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5  :   0  :   17 

40 

6     8 

2:    3:0:    4 

2: 

4  :  2 

12 

14   2 

5,3 

5:2:      8 

42 

6  15 

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6  :  0 

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15    2 

8,8 

5  :  3 :  20 

44 

7 

2:    5:3:     0 

2: 

7  :   2 

0 

16   2 

12,2 

6  :    1:  11 

48 

7  14 

2:     8:1:18 

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10  :   1 

10 

17    2 

15,7 

6:3:      2 

52 

8     4 

2:11:0:14 

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19,1 

7  :  0:  15 

54 

8  11 

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2:2: 

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56 

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78 

12     9 

4:    4:2:21 

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7:3: 

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18, 

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84 

13     8 

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20,5 

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128 

20     8 

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2, 

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136 

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1 

2 

3            I  4"l 

5 

6 

~       7            1 

Ghap.  2.]      RULES  AND  CALCULATIONS.  ±8i 


Use  of  the  Jbregoing  Table. 

Suppose  you  are  making  a  cog-wheel  with  &6  cogs; 
look  for  the  number  in  the  1st  or  4th  column,  and  against 
it,  ill  the  2d  or  5th  column,  you  find  10,  11 ;  that  is,  10 
steps  of  the  pitch  (you  use)  on  a  straight  line,  and  11  of 
22  equal  parts  of  said  pitch  added,  makes  the  radius  that 
is  to  describe  the  pitch  circle. 

The  3d,  6th  and  7th  columns,  contain  the  radius  in 
feet,  inches,  quarters,  and  22  parts  of  a  quarter ;  which 
may  be  made  use  of  in  roughing  out  timber,  and  fixing 
the  centres  that  the  wheels  are  to  run  in,  so  that  they  may 
gear  to  the  right  depth;  but,  on  account  of  the  difierence 
in  the  parts  of  the  same  scales  or  rules,  and  the  difficulty 
of  setting  the  compasses  exactly,  they  can  never  be  true 
enough  for  the  pitch  circles. 

RULE  COxMMONLY  PRACTISED. 

Divide  the  pitch  into  1 1  equal  parts,  and  take  in  youF 
compasses  7  of  those  parts,  and  step  on  a  straight  line, 
counting  4  cogs  for  every  step,  until  you  come  up  to 
the  number  in  your  wheel ;  if  there  be  an  odd  one  at 
last,  take  1-4  of  a  step,  if  2  be  left,  take  1-2  of  a  step, 
if  3  be  left,  take  8-4  of  a  step,  for  them;  and  these  steps, 
added,  makes  the  radius  or  sweep-staff  of  the  pitch  circle : 
but  on  account  of  the  difficulty  of  making  these  divisions 
sufficiently  exact,  there  is  little  truth  in  this  rule — and 
where  the  number  of  cogs  are  few,  it  will  make  the  dia- 
meter too  short,  for  the  reason  mentioned  before. 

The  following  geometrical  rule  is  more  true  and  con- 
venient, in  some  instances. 

RULE. 

Draw  Uie  line  AB,  plate  IV.  fig.  34,  and  draw  the 
line  0,2S  at  random;  then  take  the  pitch  in  your  com- 
passes, and  beginning  at  the  point  22,  step  11  steps  to- 
wards A,  and  3  1-2  steps  to  point  X,  towards  O;  draw 
the  line  AC  through  the  point  X ;  draw  the  line  DC 
parallel  to  AB;  and,  without  having  altered  your  com- 

A  a 


186  RULES  AND  CALCULATIONS.      [Chap.  2. 

passes,  begin  at  point  O,  and  step  both  ways,  as  you  did 
on  AB;  then,  from  the  respective  points,  draw  the  cross 
lines  parallel  to  0,22 ;  and  the  distance  from  the  point, 
where  they  cross  the  line  AC,  to  the  line  AB,  will  be 
the  radius  of  the  pitch  circles  for  the  number  of  cogs 
respectively,  as  in  the  figure.  If  the  number  of  cogs  be 
odd,  say  21,  the  radius  will  be  between  20  and  22. 

This  will  also  give  the  diameter  of  all  wheels,  that 
have  few  cogs,  too  short ;  but  where  the  number  of  cogs, 
is  above  twenty,  the  error  is  imperceptible. 

All  these  rules  are  founded  on  the  proportion,  as  %% 
is  to  7,  so  is  the  circumference  to  the  diameter. 


ART.    77' 
A  TABLE  OF  ENGLISH  DRY  MEASURE. 

Solid" 

mci-.es.        X  The  bushel  contains  SI 50,4 


.3  j.6 1  Pint.       X  solid  inches.    Therefore,  to 


268,8  I   8  I  Gallon,  x^  mcasurc  the  contents  of  any 

|215.,4|64|8TrTT^^^N  §^^"^^'    ^^^^    ^^^^    following 

RULE. 

Multiply  its  length  by  inches,  by  its  breadth  in  inches, 
and  that  product  by  its  height  in  inches,  and  divide  the 
last  product  by  3150,4,  and  it  will  quote  the  bushels  it 
contains. 

But  to  shorten  the  work  decimally;  because  2150,4? 
solid  inches  are  1,244  solid  feet,  multiply  the  length, 
breadth,  and  height  in  feet,  and  decimal  j^arts  of  a  foot 
by  each  other,  and  divide  by  l,2i44;  and  it  will  quote  the 
contents  in  bushels. 

EXAMPLE. 

Given,  a  garner  6,25  feet  long,  3,5  feet  wide,  10,5  feet 
high;  required,  its  contents  in  bushels.  Then,  6,25 
multiplied  by  3,5  and  10,5,  is  equal  to  229,687;  which, 
divided  by  1,244,  quotes  184  bushels  and  6  tenths. 


Chap.  2.]       RULES  AND  CALCULATIONS.  187 

To  find  the  contents  of  a  hopper,  take  the  following 

RULE. 

Multiply  the  length  by  the  width  at  the  top,  and  that 
product  by  one-  third  of  the  depth,  measuring  to  the  very 
point,  and  divide  by  the  contents  of  a  bushel,  either  in 
inches  or  decimals,  as  you  have  wrought,  and  the  quo- 
tient will  be  the  contents  in  bushels. 

EXAMPLE. 

Given,  a  hopper  43  inches  square  at  top,  and  S4)  inches 
deep;  required,  the  contents  in  bushels. 

Then  IS  multiplied  by  43  and  8,  is  equal  to  14112 
solid  inches;  which,  divided,  by  2150,4,  quotes  6,56 
bushels,  or  a  little  more  than  6|  bushels. 

To  make  a  gamer  to  hold  any  given  quantity,  having 
two  of  its  sides  given,  take  the  following 

RULE. 

Multiply  the  contents  of  1  bushel  by  the  number  of 
bushels  the  garner  is  to  hold ;  then  multiply  the  given 
sides  into  each  other,  and  divide  the  first  by  the  last 
product;  and  the  quotient  will  be  the  side  wanted,  in  the 
sanie  measure  you  have  wrought  in. 

EXAMPLE. 

Given,  tu'-o  sides  of  a  garner  6,25  by  10,5  feet;  re- 
quired, the  other  side,  to  hold  184,6  bushels. 

Then,  1,244  multiplied  by  i84,6  is  equal  to  339,642; 
which,  divided  by  the  product  of  the  two  sides  65,635, 
the  quotient  is  3,5  feet  for  the  side  wanted. 

To  make  a  hopper  to  hold  any  given  quantity,  having 
the  depth  given. 

RULE. 

Divide  the  inches  contained  in  the  bushels  it  is  to 
hold,  by  1-3  the  depth  in  inches;  and  the  quotient  will 
be  the  square  of  one  of  the  sides  at  the  top  in  inches. 
Given,  the  depth  34  inches;  required,  the  sides  to  hold 
6,56  bushels. 


18g  OF  SPUR  GEARS.  [Chap.  S. 

Then,  6,56  multiplied  by  2150,4  is  equal  to  1*107,624; 
which,  divided  by  8,  quotes  1764,  the  square  root  of 
which  is  4-2  inches;  which  is  the  length  of  the  sides  of  the 
hopper  wanted. 


CHAPTER  III. 

ART.   78. 
OF  THE  DIFFERENT  KINDS  OF  GEARS,  AND  FORMS  OF  COGS. 

IN  order  to  conceive  a  just  idea  of  the  most  suitable 
form  or  shape  for  cogs  in  cog-wheels,  we  must  consider, 
that  they  describe  with  respect  to  the  pitch  circles,  a 
figure  called  Epicycloid. 

And  when  one  wheel  works  in  cogs  set  in  a  straight 
line,  such  as  the  carriage  of  a  saw- mill,  the  cogs  or 
rounds,  moving  out  and  in,  form  a  curve  figure  called  a 
Cycloid. 

To  describe  which,  let  us  suppose  the  large  circle  in 
plate  V,  fig.  37,  to  move  on  the  straight  line  from  O  to  A; 
then  the  point  O  in  its  periphery  will  describe  the  arph 
OD A,  called  a  Cycloid;  and  we  may  conceive,  by  the 
way  that  the  curve  joins  the  line,  what  should'  be  the 
form  of  the  point  of  the  cog. 

Again,  suppose  the  small  circle  to  run  round  the  large 
one;  then  the  point  o  in  the  small  circle,  will  describe 
the  arch  o  b  c,  called  an  Epicycloid ;  by  which  we  may* 
conceive  the  form  the  point  of  the  cogs  should  be.  But 
in  common  practice,  we  generally  let  the  cogs  extend 
but  a  short  distance  past  the  pitch  circle ;  so  that  the 
form  of  the  cogs  is  not  so  particular. 


ART.    79. 

OF  SPUR  GEARS. 

The  principle  of  spur  gears,  is  that  of  two  cylinders 
rolling  on  each  other^  with   their  shafts  or  axes  truly 


Ch^3.}  OF  SPUR  GEARS.  189 

parallel  to  each  other.  Here  the  touching  parts  move 
with  equal  velocity,  therefore  have  but  little  friction. 
And  to  prevent  these  cylinders  from  slipping,  we  are 
obliged  to  indent  them,  or  to  set  in  cogs.  And  here  it 
appears  to  me,  that  the  pitch  of  the  driving  wheel  should 
be  a  little  larger  than  the  leading  wheel,  for  the  follow- 
ing reasons  : 

1.  If  there  is  to  be  any  slipping,  it  will  be  much  easier 
for  the  driver  to  slip  a  little  past  the  leader,  than  for  the 
cogs  to  have  to  force  the  leader  a  little  before  the  driver ; 
which  would  be  very  hard  on  them. 

3.  If  the  cogs  should  bend  any  by  the  stress  of  the 
work  (as  they  surely  do  ;  because  lib.  falling  on  a  beam 
a  foot  square,  will  jar  it,  which  cannot  be  done  without 
bending  it  a  little)  this  will  cause  those  that  are  coming 
into  gear  to  touch  too  soon,  and  rub  hard  at  entering. 

3.  It  is  much  better  for  cogs  to  rub  hard  as  they  are 
going  out  of  gear,  than  as  they  are  coming  in  ;  because 
then  they  work  with  the  grain  of  the  wood ;  whereas,  at 
entering  they  work  against  it,  and  would  wear  much 
faster. 

The  advantage  of  this  kind  of  gear  is,  we  can  make 
the  cogs  as  wide  as  we  please,  so  that  their  bearing  may 
be  so  large  that  they  will  not  cut  each  other,  but  only 
polish  and  wear  smooth ;  therefore  they  will  last  a  long 
time. 

Their  disadvantages  are, 

1st.  That  if  the  wheels  be  of  different  sizes,  and  the 
pitch  circles  are  not  made  to  meet  exactly,  they  will  not 
run  smooth.     And, 

2d.^  We  cannot  change  the  direction  of  the  shafts  so 
conveniently. 

Fig.  38,  plate  V,  is  two  spur  wheels  working  into 
each  other ;  the  dotted  lines  shew  the  pitch  circles, 
which  must  always  meet  exactly.  The  ends  of  the  cogs 
are  made  circular,  as  is  common  ;  but  if  they  were  made 
ef  the  true  epicycloids  that  would  suit  the  size  of  the 
wheels,  they  would  work  smoother,  with  less  friction. 

Fig.  39,  is  a  spur  and  face  wheel  or  wallower  ;  whose 
pitch  circles  should  always  meet  exactly  also. 


190  •  OF  FACE  GEARS.  [Gha^a. 

The  rule  for  describing  the  sides  of  the  cogs  of  a  form 
near  the  figure  of  an  epicycloid,  is  as  follows,  viz.  De- 
scribe a  circle  a  little  inside  of  the  pitch  circle,  for  the 
point  of  your  compasses  to  be  set  in,  so  as  to  describe 
the  sides  of  the  cog  as  the  four  cogs  at  A,  Plate  V.  fig. 
38 — 39,  as  near  as  you  can  to  the  curve  of  the  epicycloid 
that  is  formed  by  the  little  wheel's  moving  round  the 
great  one ;  the  greater  the  difference  between  the  great 
and  small  wheels,  the  greater  distance  must  this  circle, 
be  inside  of  the  pitch  circle  ;  of  this  the  practitioner  is 
to  be  the  judge,  as  no  certain  rules  is  yet  formed,  that 
I  know  of.* 


ART.    80. 
OF  FACE  GEARS. 

The  principle  of  face  gears,  is  that  of  two  cylinders 
rolling  with  the  side  of  one  on  the  end  of  the  other,  their 
axes  being  at  right  angles.  Here  the  greater  the  bearing, 
and  the  less  the  diameter  of  the  wheels,  the  greater  will  be 
the  friction  ;  because  the  touching  parts  move  with  dif- 
ferent velocities,  therefore  the  fricti(3n  will  be  great. 

The  advantages  of  this  kind  of  gear  are, 

ist.  Their  cogs  stand  parallel  to  each  other ;  therefore 
moving  them  out  or  in  gear  a  little,  does  not  alter  the 

*  Mr.  Charles  Taylor's  rule  for  ascertaining  the  true  cycloidical  or  epi- 
cycloidical  form  for  the  point  of  cogs. 

-Vl  ike  a  sepfment  of  the  pitch  circle  of  each  wheel,  which  gear  into  each 
other;  fasten  one  to  a  plane  surface,  and  roll  tlie  other  roinid  it  as  shewn, 
plaie  V,  fig.  37,  art.  79,  and  with  a  point  in  the  moveable  segment,  describe 
the  epicycloid  o  b  c,  set  off  at  tlie  end  o  one-fourth  part  of  the  pitch  for  the 
length  of  the  cog  outside  of  the  pitch  circle  Then  fix  the  compasses  at 
such  an  opening,  that  with  one  leg  tliereof  in  a  certain  point  (to  be  found 
by  repeated  trials,)  the  other  leg  will  trace  the  epicycloid  from  the  pitch 
circle  to  the  end  of  the  cog:  preserve  the  set  of  the  con. passes,  and  through 
the  pomt  where  the  fixed  leg  stood,  sweep  a  circle  from  the  centre  of  the 
wherl,  in  which  set  one  pomt  of  the  compasses  to  describe  the  point  of  all 
the  cogs  of  that  wheel  whose  segment  'vas  made  fast  to  the  plane 

If  the  wheels  be  bevel  gear,  this  rule  may  be  used  to  find  the  true  form 
fif  both  the  outer  and  inner  ends  of  the  cogs,  especially  if  the  cogs  be  long, 
as  the  epicycloid  is  different  in  different  circles.  In  making  cast-iron 
wheels,  it  is  absolutely  necessary  to  attend  to  forming  the  cogs  to  the  true 
epicycloidical  figure,  without  which  they  cannot  work  smooth  and  easy. 

The  same  rule  serves  for  ascertaining  the  cycloidical  form  of  a  right  line 
of  cogs,  such  as  those  of  a  saw-mill  carriage,  &c.  or  of  cogs  set  inside  of  a 
circle  or  hollow  cone;  «here  a  wiieel  works  within  a  wheel,  the  cogs  re' 
qtiire  a  very  different  shape- 


Chap.  3.]  OF  FACE  GEARS.  191 

pitch  of  the  bearing  parts  of  the  cogs,  and  they  will  run 
smoother  when  their  centres  are  out  of  place,  than  spur 
gears. 

2.    They  serve   for  changing  the   direction   of   the 
shafts. 

The  disadvantages  are, 

1st.  The  smallness  of  the  bearing,  so  that  they  wear 
0ut  very  fast.* 

2d.  Their  great  friction  and  rubbing  of  parts. 

The  cogs  for  small  wheels  are  generally  round,  and 
put  in  with  round  shanks.  Great  care  should  be  taken 
in  boring  the  holes  for  the  cogs,  with  a  machine  to  direct 
the  auger  straight,  that  the  distance  of  the  cogs  may  be 
equal,  without  dressing.  And  all  the  holes  of  all  the 
small  wheels  in  a  mill  should  be  bored  with  one  auger, 
and  made  of  one  pitch  ;  then  the  miller  may  keep  by 
him  a  quantity  of  cogs  ready  turned,  to  a  gauge  to  suit 
the  auger,  and  when  any  fail,  he  can  drive  out  the  old 
ones,  and  put  in  a  new  set,  without  much  loss  of  time. 

Fig.  40,  plate  V,  represents  a  face  cog-wheel  working 
into  a  trundle ;  shewing  the  necessity  of  having  the  cor- 
ners of  the  sides  of  the  cogs  sniped  off  in  a  cycloidical 
form,  to  give  liberty  for  the  rounds  to  enter  between  the 
cogs,  and  pass  out  again  freely.  To  describe  the  sides 
of  the  cogs  of  the  right  shape  to  meet  the  rounds  when 
they  get  fairly  into  gear,  as  at  c,  there  must  be  a  circle 
described  on  the  ends  of  the  cogs,  a  little  outside  of  the 
pitch  circle,  for  the  point  of  the  compasses  to  be  set  in, 
to  scribe  the  ends  of  the  cogs  ;  for  if  the  point  be  set  in 
the  pitch  circle,  it  will  leave  the  inner  corners  too  full, 
and  make  the  outer  ones  too  scant.  The  middle  of  the 
cog  is  to  be  left  straight  from  bottom  to  top,  or  nearly  so, 
and  the  side  nearly  flat  at  the  distance  of  half  the  diame- 
ter of  the  round  from  the  end,  the  corners  only  being 
sniped  off  to  make  the  ends  of  the  shape  in  the  figure ; 
because  when  the  cog  comes  into  gear  fully,  as  at  c, 
there  is  the  chief  stress,  and  there  the  bearing  should  be 

•  Fnr  if  ihe  bearing  of  the  cogs  be  smull,  and  the  stress  so  great  that 
they  cut  one  another,  iliey  will  wear  exce-ilingly  fast;  but  if  it  be  so  large, 
and  tiie  stress  so  light,  that  they  only  polish  one  another,  they  will  lasc 
very  long. 


192  OF  BEVEL  GEARS.  {Chap.  3. 

as  large  as  possible.  The  smaller  the  cog-wheel,  the 
larger  the  trundle,  and  the  wider  the  cogs,  the  more  will 
the  corners  require  to  be  sniped  off.  Suppose  the  cog- 
wheel to  turn  from  40  to  b,  the  cog  40,  as  it  enters,  will 
bear  on  the  lower  corner,  unless  it  be  sufficiently  sniped 
off;  when  it  comes  to  c,  it  will  be  fully  in  gear,  and  if  the 
pitch  of  the  cog-wheel  be  a  litde  larger  than  that  of  the 
trundle,  the  cog  a  will  bear  as  it  goes  out,  and  let  c  fairly 
enter  before  it  begins  to  bear. 

Suppose  the  plumb  line  A  B  to  hang  directly  to  the 
centre  of  the  cog-wheel,  the  spindle  is  (by  many  mill- 
wrights) set  a  little  before  the  line  or  centre,  that  the 
working  round  or  stave  of  the  trundle  may  be  fair  with 
said  line,  and  meet  the  cog  fairly  as  it  comes  to  bear  :  it 
also  causes  the  cogs  to  enter  with  less,  and  go  out  with 
more  friction.  Whether  there  be  any  real  advantage  in 
thus  setting  the  spindle  foot  before  the  centre  plumb 
line,  does  not  seem  determined. 


ART.    81. 

OF  BEVEL  GEARS. 

The  principle  of  bevel  gears,  is  that  of  two  cones 
rolling  on  the  surface  of  each  other,  their  vertexes  meet- 
ing in  a  point,  as  at  A,  fig.  41,  plate  V.  Here  the  touch- 
ing surfaces  move  with  equal  velocities  in  every  part  of 
the  cones ;  therefore  there  is  but  little  friction.  These 
cones  being  indented,  or  fluted  with  teeth  diverging  from 
the  vertex  to  the  base,  to  prevent  them  from  slipping, 
become  bevel  gear  ;  and  as  these  teeth  are  very  small  at 
the  point  or  vertex  of  the  cone,  they  may  be  cut  off  2  or 
3  inches  from  the  base,  as  19  and  25,  at  B ;  they  then 
have  the  appearance  of  wheels. 

To  make  these  wheels  of  a  suitable  size  for  any  num- 
ber of  COSTS  vou  choose  to  have  to  work  into  one  another, 
take  the  following 

RULE. 

Draw  lines  to  represent  your  shafts,  in  the  direction 
they  are  to  be,  with  respect  to  each  other,  to  intersect  at 


Chap.  3.]  OF  BEVEL  GEARS.  19:> 

A  ;  then  take  from  any  scale  of  equal  parts,  either  feet, 
inches  or  quarters,  &c.  as  many  as  your  wheels  are  to 
have  cogs,  and  at  that  distance  from  the  respective  shafts, 
draw  the  dotted  lines  a  b,  c  d,  for  2i  and  20  cogs  ;  and 
from  where  they  cross  at  e,  draw  e  A.  On  this  line, 
which  makes  the  right  bevel,  the  pitch  circles  of  the 
wheels  will  meet,  to  contain  that  proportion  of  cogs  of 
any  pitch. 

Then  to  determine  the  size  of  the  wheels  to  suit  any 
particular  pitch,  take  from  the  table  of  pitch  circles,  the 
radius  in  measures  of  the  pitch,  and  apply  it  to  the  centre 
of  the  shaft,  and  the  bevel  line  A  e,  taking  the  distance 
at  right  angles  with  the  shaft ;  and  it  will  show  the  point 
in  which  the  pitch  circles  will  meet,  to  suit  that  particu- 
lar pitch. 

By  the  same  rule,  the  sizes  of  the  wheels  at  B  and  C 
are  found. 

These  kind  of  wheels  are  frequently  made  of  cast 
metal,  and  do  exceedingly  well. 

The  advantages  of  this  kind  of  gear  are, 

1.  They  have  very  little  friction,  or  sliding  of  parts. 

2.  We  can  make  the  cogs  of  any  width  of  bearing  we 
choose  ;  therefore  they  will  wear  a  great  while, 

3.  By  them  we  can  set  the  shafts  in  any  direction  de- 
sired, to  produce  the  necessary  movements. 

Their  disadvantages  are, 

1.  They  require  to  be  kept  exactly  of  the  right  depth 
in  gear,  so  that  the  pitch  circles  just  meet,  else  they  will 
not  run  smooth,  as  is  the  case  with  spur  gears. 

2.  They  are  expensive  to  make  of  wood ;  therefore 
few  in  this  country  use  them. 

;  The  universal  joint,  as  represented  fig.  43,  may  be 
applied  to  communicate  motion,  instead  of  bevel  gear, 
where  the  motion  is  to  be  the  same,  and  the  angle  not 
more  than  30  or  40  degrees.  This  joint  may  be  con- 
structed by  a  cross,  as  in  the  figure,  or  by  4  pins  fasten- 
ed at  right  angles  on  the  circumference  of  a  hoop  or 
solid  ball.  It  may  sometimes  serve  to  communicate  the 
motion,  instead  of  9  or  3  face  wheels.  The  pivots  at  the 
end  of  the  cross  play  in  the  ends  of  the  semicircles.     It 

Bb 


194  OF  MATCHING  WHEELS,  &c.         [Chap.S. 

is  best  to  screw  the  semicircles  to  the  blades,  that  they 
may  be  taken  apart.  • 


ART.    83. 
OF  MATCHING  WHEELS,  TO  MAKE  THE  COGS  WEAR  EVEN- 

Great  care  should  be  taken  in  matching  or  coupling 
the  wheels  of  a  mill,  that  their  number  of  cogs  be  not 
such  that  the  same  cogs  will  often  meet ;  because  if  two 
soft  ones  meet  often,  the)?-  will  both  wear  away  faster 
than  the  rest,  and  destroy  the  regularity  of  the  pitch ; 
whereas  if  they  are  continually  changing,  they  will  wear 
regular,  even  if  they  are  at  first  a  little  irregular. 

For  finding  how  often  they  will  revolve  before  the 
same  cogs  meet  again,  take  the  following 

RULE. 

L  Divide  the  cogs  in  the  greater  wheel  by  the  cogs 
in  the  lesser;  and  if  there  be  no  remainder,  the  same 
cogs  will  meet  once  every  revolution  of  the  great  wheel. 

2.  If  there  be  a  remainder,  divide  the  cogs  in  the 
lesser  wheel  by  the  said- remainder  ;  and  if  it  divide  them 
equally,  the  quotient  shows  how  often  the  great  wheel 
Avill  revolve  before  the  same  cogs  meet. 

3.  But  if  it  will  not  divide  equally,  then  the  great 
wheel  will  revolve  as  often  as  there  are  cogs  in  the  small 
wheel,  and  the  small  wheel  as  often  as  there  are  cogs  in 
the  large  wheel,  before  the  same  cogs  meet :  oftener  they 
can  never  be  made  to  change. 

EXAMPLES. 

1.  Given,  wheels    13  and    17   cogs ;  required,   how 
often  each  will  revolve  before  the  same  cogs  meet  again. 
Then  13)17(1 
13 

4)13(3 

12  Answer, 

—  Great  wheel  13,  and 

1  Small    do.    17  revs. 


Chap.  3.]  OF  ROLLING  SCREENS  AND  FANS.    195 


ART.   83. 

THEORY  OP  ROLLING  SCREENS  AND  FANS,  OR  WIND  MILLS  FOR 
SCREENING  AND  FANNING  THE  WHEAT  IN  MILLS. 

Let  fig.  42,  plate  V,  represent  a  rolling  screen  and 
fan,  fixed  for  cleaning  wheat  in  a  merchant- mill.  DA 
the  screen,  AF  the  fan,  AB  the  wind  tube,  3  feet  deep 
from  A  to  b,  and  4<  inches  wide,  in  order  that  the  grain 
may  have  a  good  distance  to  fall  through  the  wind,  to 
give  time  and  opportunity  for  the  light  parts  to  be  carried 
forward  before  the  heavy  parts.  Suppose  the  tube  to  be 
of  equal  depth  and  width  the  whole  of  its  length,  except 
where  it  communicates  with  the  tight  boxes  or  garners 
under  it,  viz.  c  for  the  clean  wheat,  S  for  the  screenings 
and  light  \\  heat,  and  C  for  the  cheat,  chaff,  &c.  Now  it 
is  evident,  if  wind  be  by  the  fan  drove  into  the  tube  at 
A,  that  if  it  can  escape  no  where,  it  will  pass  on  to  B, 
with  the  same  force  as  at  A,  let  the  tube  be  of  any  length 
or  direction;  and  any  thing  which  it  will  move  at  A,  it 
W'ill  carry  out  at  B,  if  the  tube  be  of  an  equal  size  all  the 
way. 

It  is  also  evident,  that  if  we  shut  the  holes  of  the  fan 
at  A  and  F,  and  let  no  wind  into  it,  none  can  be  forced 
into  the  tube  ;  hence,  the  best  way  to  regulate  the  blast 
is,  to  fix  shutters  sliding  at  the  air  holes,  to  give  more 
or  less  feed  or  air  to  the  fan,  so  as  to  produce  a  blast 
sufficient  to  clean  the  grain. 

The  grain  is  let  into  the  screen  at  D,  into  the  inmost 
cylinder,  in  a  small  stream.  The  screen  consists  of  tuo 
cylinders  of  sieve  wire,  the  inmost  one  has  the  meshes 
so  open,  as  to  pass  all  the  wheat  through  it  to  the  outer 
one,  retaining  only  the  white  caps,  large  garlic,  and  every 
thing  larger  than  the  grain  of  the  wheat,  which  falls  out 
at  the  tail  A. 

The  outer  cylinder  is  so  close  in  the  mesh,  as  to  re- 
tain all  good  wheat,  but  sift  out  the  cheat,  cockle,  small 
wheat,  garlic,  and  every  thing  less  than  good  grains  of 
wheat ;  the  wheat  is  delivered  out  at  the  tail  of  the  outer 
cylindef,  which  is  not  quite  as  long  as  the  inner  one. 


196    OF  ROLLING  SCREENS  AND  FANS.  [Chap.  3. 

where  it  drops  into  the  wind  tube  at  a,  and  as  it  falls 
from  a  to  b,  the  wind  carries  off  every  thing  lighter  than 
good  wheat,  viz,  cheat,  chaff,  light  garlic,  dust,  and  light 
rotten  grains  of  wheat ;  but,  in  order  to  effect  this  more 
completely,  it  should  fall  at  least  3  feet  through  the  cur- 
rent of  wind. 

The  clean  wheat  falls  into  the  funnel  b,  and  thence 
into  the  garner  c,  over  the  stones.  The  light  wheat, 
screenings,  &c.  fall  into  garner  S,  and  the  chaff  settles 
into  the  chaff  room  C.  The  current  slackens  passing 
over  this  room,  and  drops  the  chaff,  but  resumes  its  full 
force  as  soon  as  it  is  over,  and  carries  out  the  dust 
through  the  wall  at  B.  To  prevent  the  current  from 
slackening  too  much  as  it  passes  over  S  and  c,  and  un- 
der the  screen,  make  the  passages,  where  the  grain 
come  in  and  goes  out,  as  small  as  possible,  not  more 
than  half  an  inch  wide,  and  as  long  as  necessary.  If  the 
wind  escapes  any  where  but  at  B,  it  defeats  the  scheme, 
and  carries  out  the  dust  into  the  mill.  Or  fix  valves  to 
shut  the  passages  by  a  weight  or  spring,  so  that  the 
weight  of  the  wheat,  &c.  falling  on,  will  open  them  just 
enough  to  let  it  pass,  without  suffering  any  wind  to 
escape.* 

Note,  the  fan  is  set  to  blow  both  the  wheat  and  screen- 
ings, and  carry  the  dust  out. 

Note  also.  That  the  wind  cannot  escape  into  the  gar- 
ners or  screen  room,  if  they  are  tight ;  for  as  soon  as 
they  are  full,  no  more  can  enter. 

By  attending  duly  to  the  foregoing  principle,  we  may 
fix  fans  to  answer  our  purposes. 

The  principal  things  to  be  observed  in  fixing  serenes 
and  fans,  are, 

1.  Give  the  screen  1  inch  to  the  foot  fall,  and  between 
15  and  18  revolutions  in  a  minute. 

2.  To  make  the  fan  blow  strong  enough,  let  the  wings 
be  3  feet  wide,  20  inches  long,  and  revolve  UrO  times 
in  a  minute. 

3.  Then  regulate  the  blast,  by  giving  more  or  less 
feed  of  wind. 

•  This  1  have  from  Timothy  Kirk,  being  one  principle  of  his  improved 
fan. 


Chap.  4.]  OF  GUDGEONS.  %^7 

4.  Leave  no  place  for  the  wind  to  escape,  but  at  the 
end  through  the  wall. 

5.  Wherever  you  want  it  to  blow  hardest,  there  make 
the  tube  narrowest. 

6.  Where  you  want  the  chaff  and  cheat  to  fall,  there 
make  the  tube  sufficiently  wider. 

7.  Make  them  blow  both  the  wheat  and  screenings, 
and  carry  the  dust  clear  out  of  the  mill. 

8.  The  wind  tube  may  be  of  any  length,  and  either 
crooked  or  straight,  as  may  best  suit ;  but  no  where  less 
than  where  the  wheat  falls. 


CHAPTER  IV. 
ART.   84. 

OF  GUDGEONS,  THE  CAUSE  OF  THEIR  HEATING  AND  GETTING 
I-OOSE,  AND  REMEDIES  THEREFOR. 

THE  cause  of  gudgeons  heating,  is  the  excessive 
friction  of  their  rubbing  parts,  which  generates  the  heat 
in  proportion  to  the  weight  that  passes  the  rubbing  sur- 
faces together,  and  the  velocity  with  which  they  move. 
See  art.  31. 

The  cause  of  their  getting  loose  is,  their  heating,  and 
burning  the  wood,  or  drying  it,  so  that  it  shrinks  in  the 
bands,  and  gives  the  gudgeon  room  to  work. 

To  avoid  the  effects,  we  must  remove  the  causes. 

1.  Increase  the  surface  of  contact  or  rubbing  parts, 
and,  if  possible,  decrease  their  velocity  ;  the  heat  will  not 
then  be  generated  so  much. 

S.  Conduct  the  heat  away  from  the  gudgeon  as  fast 
as  generated,  if  possible. 

To  increase  the  surface  of  contact,  without  increasing 
its  velocity,  make  the  neck  or  bearing  part  of  the  gud- 
geon  longer.  If  the  length  be  doubled,  the  weight  will 
be  sustained  by  a  double  surface,  and  velocity  the  same ; 
there  will  not  then  be  so  much  heat  generated  :  and  even 


198  OF  GUDGEONS.  fChap.  4. 

supposing  the  same  quantity  of  heat  generated,  there 
will  be  a  double  space  of  surface  exposed  to  air,  to  con- 
vey it  away.* 

To  convey  the  heat  away  as  fast  as  generated,  cause 
a  small  quantity  of  water  to  drop  slowly  on  the  gudgeon, 
to  carry  off  the  heat  by  evaporation.!  A  small  quantity 
is  better  than  a  large ;  because  it  should  be  just  suffi- 
cient to  keep  up  the  evaporation,  and  not  destroy  the 
polish  made  by  the  grease ;  which  it  will  do  if  the  quantity 
be  too  great,  and  will  let  the  bear  box  and  gudgeon  come 
in  contact;  which  will  cause  both  to  wear  away  very 
fast.J 

The  best  form  that  I  have  seen  for  large  gudgeons 
for  heavy  wheels,  is  made  of  cast  iron.  Fig.  6,  plate 
XI.  is  a  perspective  view  of  one ;  a  a  a  a,  are  four  wing« 
at  right  angles  with  each  other,  extending  from  side  to 
side  of  the  shaft.  These  wings  are  larger,  every  way, 
at  the  end  that  is  farthest  in  the  shaft,  than  at  the  outer 
end,  for  convenience  in  casting  them,  and  also  that  the 
bands  may  drive  on  tight,  one  over  each  end  of  the 
wings.  Fig.  4,  is  an  end  view  of  the  shaft,  with  the 
gudgeon  in  it,  and  a  band  on  the  end ;  these  bands,  be- 

•  To  understand  this  subject  better,  let  us  consider,  that  when  we  strike 
a  flint  with  steel,  we  choose  the  sharpest  part  of  the  flint ;  then  the  surface 
of  contact  is  so  small,  that  the  force  of  the  stroke  creates  friction  enough 
to  strike  or  generate  fire  ;  but  if  we  strike  a  thick  snjooth  part  of  the  flint, 
the  force  will  not  be  sufficient  to  strike  fire,  the  surface  being  too  large. 
Hence  we  ma}-  conclude,  that  the  smaller  the  rubbing  surface,  the  greater 
the  heat  ;  and  if  tiie  surface  was  so  small  as  to  strike  fire  continually,  it 
would  be  very  difiicult  to  keep  the  gudgeon  cool-  If  a  gudgeon  heats  at  3 
inches  bearing  on  the  box,  lengthen  it  to  6  or  8  inches.  I  have  seen  them 
in  use  from  2  1  2  to  10  inches  bearing  on  the  box ;  and  those  who  had  the 
longest  (being  men  of  the  greatest  experience  in  the  milling  business) 
accounted  their  length  to  be  a  good  remedy  against  the  heating. 

f  Water  is  a  great  conductor  of  heat,  and  wonderful  is  the  effect  of  the 
principle  of  evaporation,  in  carrying  off  the  heat  from  bodies;  every  par- 
tide  of  water  that  evaporates,  carries  ofi"  a  quantity  of  heat  with  it.  Dr. 
Franklin  asserts,  that  by  evaporation  a  man  could  be  froze  to  death  the 
warmest  day  in  summer. 

t  The  grease  operates  in  lessening  friction,  perhaps  in  three  ways.  1st. 
The  particles  of  the  grease,  by  filling  up  the  pores  of  the  box  and  gudgeon, 
makes  the  sliding  surface  more  perfectly  smooth.  2.  The  particles  of 
grease  act  as  rollers  between  the  sliding  surfaces.  3-  It  destroys  the 
cohesion  that  might  otherwise  take  place  between  the  surfaces-  See  art. 
31,  and  33- 

Oil  is  said  to  answer  best  for  spindle  feet  and  step  gudgeons,  tallow  for 
common  gudgeons,  and  black  lead  mixt  with  tallow  for  cogs,  which  forms 
a  glossy  polish  on  them  that  will  wear  a  long  time- 


Chap.  4.]  OF  GUDGEONS.  199 

ing  put  on  hot,  become  very  tight  as  they  cool,  and  if 
the  shaft  is  dry  will  not  get  loose  ;  but  will  if  it  is  ^:eei\ : 
but  by  driving  a  few  wedges  along  side  of  each  wing,  it 
can  be  easily  fastened,  by  any  ordinary  hand,  without 
danger  of  moving  it  much  from  the  centre. 

One  great  use  of  these  wings  is,  to  convey  away  thse 
heat  from  the  gudgeon  to  the  bands,  which  are  in  con- 
tact with  the  air ;  and  by  thus  distributing  the  heat 
through  so  much  metal,  with  so  large  a  surface  exposed 
to  the  air,  the  heat  is  carried  off  as  fast  as  generated ; 
therefore  can  never  accumulate  to  a  degree  sufficient  to 
burn  loose,  as  it  will  often  do  in  common  gudgeons  of 
wrought  iron.  Wood  will  not  conduct  the  heat  as  well 
as  the  wings  of  metal ;  therefore  it  accumulates  in  the 
small  space  of  the  gudgeon,  to  such  a  degree  as  to  burn 
loose. 

These  gudgeons  should  be  made  of  the  best  hard 
metal,  well  refined,  in  order  that  they  may  wear  well, 
and  not  be  subject  to  break  ;  but  of  this  there  is  but  little 
danger,  if  the  metal  is  good  :  should  it  prove  to  be  the 
case,  I  propose  to  have  wings  cast  separate  from  the 
neck,  as  represented  by  fig.  4  :  where  the  inside  light 
square  shows  a  mortise  for  the  steeled  gudgeon,  Plate 
XI.  fig.  8,  to  be  fitted  into,  with  an  iron  key  behind  the 
wings,  to  draw  the  gudgeon  in  tight,  if  ever  it  should 
work  loose ;  by  which  means  it  may  be  taken  out,  at  any 
time,  to  repair. 

This  plan  would  do  well  for  step  gudgeons  for  heavy 
upright  shafts,  such  as  tub-mills,  &c. 

When  the  neek  is  cast  with  the  wings,  the  square  part 
in  the  shaft  need  not  be  larger  than  the  light  square  re- 
presenting the  mortise.* 

*  Grease  of  any  kind  used  to  the  drill,  in  boring  cast  iron,  prevents  it 
from  cutting,  but  on  the  contrary  will  make  it  cut  wrought  iron  or  steel 
much  faster  This  quality  in  cast  iron  renders  it  most  suitable  for  gud- 
geons, and  may  be  the  principal  cause  why  cast  iron  gudgeons  have  proved 
much  better  than  any  one  expected.  Several  of  the  most  experienced 
and  skilful  mill-wrights  and  millers  do  assert  that  they  have  experienced 
cast  gudi^eons  to  run  on  cast  boxes  better  than  on  stone  or  brass,  in  one 
instance  carrying  heavy  overshot  wheels  which  turned  seven  feet  mill- 
stones. They  have  run  ten  years,  doing  much  work,  and  have  hardly 
worn  off  the  sand  marks  ;  may  we  not  expect  them  to  last  ten  times  a». 


2Q0  ON  BUILDING  MILL-DAMS.       [Chap.  5. 

CHAPTER  V. 
ART.   85, 

ON  BUILDING  MJLL-DAIMS,  LAYJNG  FOUNDA.TIONS,  AND 
BUILDING  MILL  WALLS. 

THERE  are  several  things  to  be  considered,  and 
dangers  to  be  guarded  against,  in  building  mill-dams. 

i.  Construct  them  so,  that  the  water,  tumbling  over 
them,  cannot  undermine  their  foundations  at  the  lower 
side.* 

2.  So  that  heavy  logs,  large  pieces  of  ice,  &c.  float- 
ing down,  cannot  catch  against  any  part  of  them,  but  slide 
easily  over.f 

long,  and  make  up  100  years  ?  In  other  instances  they  have  worn  out  in  a 
few  days,  and  let  the  wheel  drop,  owing  no  doubt,  to  theif  being  made  of 
unsuitable  metal  op  wrongly  tempered. 

•  If  you  have  not  a  foundation  of  solid  rocks,  or  so  heavy,  that  the  wa- 
ter tumbling  over,  will  never  move  them,  there  should  be  such  a  founda- 
tion made  with  great  stones,  not  lighter  than  mill-stones  (if  the  stream 
is  heavy,  and  the  tumble  great)  well  laid,  as  low  and  close  as  possible, 
with  their  upstream  end  lowest,  to  prevent  any  thing  from  catching  under 
them.  But  if  the  bottom  is  sand  or  clay,  make  a  foundation  of  the  trunks 
of  long  trees,  laid  close  together  on  the  bottom  of  the  creek,  with  their 
butt  ends  down  stream,  as  low  and  close  as  possible,  across  the  whole  tum- 
bling space.  On  these  may  be  built  the  dam,  either  of  stone  or  wood, 
leaving  12  or  15  feet  below  the  breast  or  fall,  for  the  water  to  fall  upon. 
See  fig.  3,  plate  X,  which  is  a  front  view  of  a  log  dam,  showing  the  posi- 
tion of  the  logs,  also  of  the  stones  in  the  abutments. 

f  if  the  dam  is  built  of  timber  and  small  stones,  &c.  make  the  breast 
perpendicular  of  straight  logs,  laid  close  one  upon  another,  putting  the 
largest,  longest,  and  best  logs  on  the  top  ;  make  another  wall  of  logs  12 
or  15  feet  upstream,  laying  them  close  together,  to  prevent  lamprey  eels 
from  working  through  them,  not  so  high  as  the  other,  by  3  feet;  tie  these 
walls  together,  at  every  6  feet,  with  cross  logs,  with  the  butts  down 
stream,  dovetailed  and  bolted  strongly  to  the  logs  of  the  lower  wall,  espe- 
cially the  upper  log,  which  should  be  strongly  bolted  down  lo  them.  The 
spaces  between  these  log  walls,  are  to  be  filled  up  with  stones,  gravel.  Sec. 
Choose  a  dry  season  for  this  work ;  then  the  water  will  run  through  the 
lower  part  while  you  build  the  upper  part  tight. 

To  prevent  any  thing  from  catching  against  the  top  log,  flag  the  top  of  the 
dam  with  broad  or  long  stones,  laying  the  downstream  end  on  the  upstream 
side  of  the  log,  to  extend  a  little  above  it,  the  other  end  lowest,  so  that  the 
next  tier  of  stones  will  lap  a  little  over  the  first;  still  gettmg  lower  as  you 
advance  upstream.  This  will  ;■  lance  logs,  &c.  over  the  dam,  without  catch- 
ing against  any  thing.  If  suitable  stones  cannot  be  had,  I  would  recommend 
strong  plank,  or  small  logs,  laid  close  together,  with  both  ends  pinned  to  the 
top  logs  of  the  wall,  the  upstream  end  being  3  feet  lower  than  the  other: 
But  if  plank  is  to  be  used,  there  need  only  be  a  strong  frame  raised  on  the 


Chap.  5.]     ON  BUILDING  MILL-DAMS.  201 

3.  So  that  the  pressure  or  force  of  the  current  of  the 
water  will  press  their  parts  more  firmly  together.* 

^.  Give  them  a  sufficient  tumbling  space  to  vent  all 
the  water  in  time  of  freshets.f 

5.  Make  the  abutments  so  high,  that  the  water  will 
not  overflow  them  in  time  of  freshets. 

6.  Let  the  dam  and  mill  be  a  sufficient  distance  apart ; 
so  that  the  dam  will  not  raise  the  water  on  the  mill,  in 
time  of  high  floods.  J 

foundation  logs,  to  support  the  plank  or  the  timber  it  is  pinned  to.  See  a 
side  view  of  this  frame,  %.  45,  plate  IV.  Some  plank  the  breast  to  the 
front  posts,  and  fill  the  hollow  space  with  stone  and  gravel ;  but  this  may 
be  omitted,  if  the  foundation  logs  are  sufficiently  long  upstream,  under  the 
dam,  to  prevent  the  whole  from  floating  away.  Stone  first,  and  then  gravel> 
sand,  and  clay,  are  to  be  filled  in  above  this  frame,  so  as  to  stop  the  water. 
Jf  the  abutments  are  well  secured,  the  dam  will  stand  well. 

General  Ira  Allen,  of  the  state  of  Vermont,  ascertained  by  experiment, 
that  a  plank  laid  in  a  current  of  water,  with  the  upstream  end  lowest  set 
at  an  angle  of  22  1-2  degrees  with  the  horizon  or  current  of  the  water,  will 
he  held  firmly  to  its  place  by  the  force  of  the  current,  and  in  this  position 
at  requires  the  greatest  force  to  remove  it,  and  the  stronger  the  current 
"the  firmer  it  is  held  to  its  place,  that  is,  supposing  there  remains  a  partial 
■vacuum  under  the  plank,  this  points  out  the  best  position  for  the  breast  of 
idams. 

*  If  the  dam  is  built  of  stone,  make  it  in  the  form  of  an  arch  or  semicircle, 
Standing  upstream,  and  endeavour  to  fix  strong  abutments  on  each  side,  to 
support  the  arch  ;  then,  in  laying  the  stones,  put  the  widest  end  upstream, 
and  the  more  they  are  drove  downstream,  the  tighter  they  will  press  to- 

fftther.  All  the  stones  of  a  dam  should  be  laid  with  their  upstream  ends 
owest,  and  the  other  end  lapped  over  the  preceding,  in  manner  of  the 
ehingles  or  tiles  of  a  house,  to  glance  every  thing  smoothly  over,  as  at  the 
tside  3,  of  fig.  3,  plate  X.  The  breast  may  be  built  up  with  stone,  either  on 
(a  good  rock  or  log  foundation,  putting  the  best  m  front,  leaning  a  little 
upstream,  and  on  the  top  lay  one  good  log,  and  another  15  feet  upstream 
en  the  bottom,  to  tie  the  top  log  to,  by  several  logs,  with  good  butts,  down* 
stream,  dovetailed  and  bolted  strongly,  both  at  bottom  and  top  of  the  top 
»nd  upstream  logs  ;  fill  in  between  them  with  stone  and  gravel,  laying  large 
©tones  slanting  next  the  top  log,  to  glance  any  thing  over  it.  This  will  be 
much  better  than  to  build  all  of  stone  ;  because  if  one  at  top  give  way,  the 
fcreach  will  increase  rapidly,  and  the  whole  go  down  to  the  bottom. 

t  It  the  tumbling  space  is  not  long  enough,  the  water  will  be  apt  to 
overflow  the  abutments,  and  if  they  are  earth  or  loose  stones,  they  will  be 
broken  down,  and  perhaps  a  very  great  breach  made.  If  the  dam  is  of 
logs,  the  abutments  had  best  be  made  of  stone,  laid  as  at  the  side  3,  in 
fig.  3;  but  if  stone  is  not  to  be  had,  they  must  be  made  of  wood,  although 
subject  lo  rot  soon,  being  above  water. 

+  I  have,  in  many  instances,  seen  the  mill  set  so  close  to  the  dam,  that 
the  pier  head  or  forebay  was  in  the  bre:st;  so  that  in  case  of  a  leak  or 
breach  about  the  forebay  or  mill,  there  is  no  chance  of  shutting  off  the 
water,  or  conveying  it  another  way ;  but  all  must  be  left  to  its  fate.  The 
mill  is  frequently  broken  down,  and  carried  away;  even  the  mill  stones 
are  carried  a  considerable  distance  down  the  stream,  and  sometimes  buried 
under  the  sand,  and  never  found. 

C  C 


202  ON  BUILDING  MILL-WALLS.    [Chap;  5. 


ART.   86. 

ON  BUILDING  MILL-WALLS. 

The  principal  things  to  be  considered  in  building 
mill- walls,  are, 

1.  To  lay  the  foundations  with  good  large  stones,  so 
deep  as  to  be  out  of  danger  of  being  undermined,  in 
case  of  any  accident  of  the  water  breaking  through  at 
the  mill.* 

2.  Set  the  centre  of  gravity,  or  weight  of  the  wall,  on 
the  centi'e  of  its  foundation.  }- 

The  great  danger  of  this  error  will  appear  more  plain,  if  we  suppose  six 
mills  on  one  stream,  one  above  the  other,  each  at  the  breast  of  the  dam  ; 
and  a  great  flood  to  break  the  first  or  uppermost  dam,  say  through  the 
pierhead,  carrymg  with  it  the  mill,  stones  and  all;  this  so  increases  the 
flood,  that  it  overflows  the  next  dam,  which  throws  the  water  against  the 
mill,  and  it  is  taken  away;  the  water  of  these  two  dams  has  now  so  aug- 
mented the  flood,  that  it  carries  every  mill  before  it,  until  it  comes  to  the 
dam  of  the  sixth,  which  it  sweeps  away  also;  but  suppose  this  dam  to  be 
a  quarter  of  a  mile  above  the  mill,  which  is  set  well  into  the  bank,  the  extra 
water  that  is  thrown  into  the  canal,  runs  over  at  the  waste  left  in  its  banks 
for  the  purpose  ;  and  the  water  having  a  free  p;issage  by  the  mill,  does  not 
injure  it;  whereas,  had  it  been  at  the  breast  of  the  dam,  it  must  have  went 
away  with  the  rest-  A  case  similar  to  this,  actually  happened  in  Virginia 
in  1794;  all  the  mills  and  dams  on  Falling  Creek,  in  Chesierfield  county, 
were  carried  away  at  once,  except  the  lowest,  (Mr.  Wardrope's  :)  whose 
dam,  having  broke  the  year  before,  was  rebuilt  a  quarter  of  a  mile  higher 
up  ;  by  which  means  his  mill  was  saved. 

*  If  the  foundation  is  not  good,  but  abounding  with  quicksands,  the  wall 
cannot  be  expected  to  stand,  unless  it  be  made  good  by  driving  down  piles 
until  they  meet  the  solid  ground  :  on  the  top  of  which  may  be  laid  large 
flat  pieces  of  timber,  for  the  walls  to  be  built  on  ;  they  will  not  rot  under 
water,  totally  excluded  from  the  air. 

f  It  is  a  common  practice  to  build  walls  plumb  outside,  and  batter  them 
all  from  the  inside  ;  which  throws  the  centre  of  their  gravity  to  one  side  of 
their  base.  See  art.  14.  Therefore  if  it  settles  any,  it  will  incline  to  fall 
outwards.  Mill-walls  should  be  battered  as  much  outside,  as  to  be  equal  to 
the  offsets  inside^  to  cause  the  whole  weight  to  stand  on  the  centre  of  the 
foundation,  unless  it  stand  against  a  bank,  as  the  wall  next  the  wagon, 
in  plate  VIII.  The  bank  is  very  apt  to  press  the  wall  inwards,  unless  it 
stands  battering.  In  this  case,  build  the  side  against  the  bank  plumb, 
even  with  the  ground,  and  then  begin  to  batter  it  inwards.  The  plumb 
rules  should  be  made  a  little  widest  at  the  upper  end,  so  as  to  give  the 
wall  the  right  inclination,  according  to  its  height  ;  to  do  which, 
tiike  a  line,  the  length  equal  to  the  height  of  the  wall,  set  one  end, 
by  a  compass  point,  in  the  lower  end  of  the  plumb  rule,  and  strike 
the  plumb  line;  then  move  the  other  end  just  as  much  as  the  wall 
is  to  be  battered  in  the  whole  height:  and  it  will  show  the  inclination 
of  the  side  of  the  rule  that  will  batter  the  wall  exactly  right.  This  error 
of  building  walls  plumb  outside,  is  frequently  committed  in  building  he 
abutments  of  bridges  ;  the  consequence  is,  they  fall  down  in  a  short  lime  ; 


Chap.  5.]       ON  BUILDING  MILL-WALLS.  203 

3.  Use  good  mortar,  and  it  will,  in  time,  petrify  and 
become  as  hard  as  stone.* 

4.  Arch  over  all  the  windows,  doors,  &c. 

5.  Tie   them   well   together  by  the  timbers  of  the 
floors. 


because  the  earth  balween  the  walls  is  expanded  a  little  by  every  hard 
fropt,  and  tumbles  the  walls  over. 

•  I  have  but  little  experience  in  this ;  but  will  quote  an  experienced 
author  (George  Sample,  on  Free  Trade.)  He  says, 

"  CoNCERNiiirG  Lime,  Moktar,  and  Grout. 

"  I  have,  from  my  childhood,  been  well  acquainted  with  the  nature  of 
lime  and  sand  made  into  mortar,  of  all  sorts  that  have  been  used  in  build- 
ings in  these  countries,  and  tried  numerous  experiments  with  them.  On 
which,  together  with  what  I  have  observed  and  learned  from  old  expe- 
rienced workmen,  during  the  course  of  upwards  of  sixty  years,  I  think  I 
can  safely  affirm,  that  good  mortar,  that  is  made  of  pure  and  well-burnt 
limestone,  properly  made  up  with  sharp  clean  sand,  free  from  any  sort  of 
earth,  loam  or  mud,  will,  within  some  considerable  time,  actually  petrify, 
and,  as  it  were,  turn  to  the  consistence  of  a  stone.  I  remember  I  had  one 
of  my  remarks  from  an  old  Scotch  mason;  which  1  shall  give  you  in  his 
own  identical  words;  that  is, 

"  when  a  hundred  years  are  past  and  gane, 

*'  Then  gude  mortar  is  grown  to  a  stain  (or  stone.) 

"I  need  not  explain  what  I  mean  by  sharp  clean  sand ;  but  I  shall  giva 
you  this  one  caution,  that  it  is  better  to  put  too  much  sand  in  your  mortar, 
than  too  little.  I  know  workmen  choose  their  mortar  rich,  because  it  works 
pleasanter;  but  rich  mortar  will  not  stand  the  weather  so  well,  nor  grow 
so  hard,  as  poor  mortar  will  do.  If  it  was  all  lime,  it  would  have  no  more 
strength,  in  comparison,  than  clay." 


PART  III. 

CONTAINING 

EVANS'S  PATENTED  IMPROVEMENTS 

ON  THE 

ART  OF  MANUFACTURING   GRAIN   INTO  MEAL 
AND  FLOUR. 


INTRODUCTION. 


THESE  improvements  consist  of  the  inven- 
tion, and  various  applications,  of  the  following 
machines,  viz. 

1.  The  Elevator. 
S.  The  Conveyer. 

3.  The  Hopper-boy. 

4.  The  Drill. 

5.  The  Descender. 

Which  five  machines  are  variously  applied, 
in  different  mills,  according  to  their  construction, 
so  as  to  perform  every  necessary  movement  of 
the  grain  and  meal,  from  one  part  of  the  mill  to 
another,  or  from  one  machine  to  another,  through 
all  the  various  operations,  from  the  time  the  grain 
IS  emptied  from  the  wagoner's  bag,  or  from  the 
measure  on  board  the  ship,  until  it  is  completely 
manufactured  into  supei^fine  flour,  and  other  dif- 
fereni  qualities,  and  completely  separated,  ready 


208  INTRODUCTION. 

for  packing  into  barrels,  for  sale  or  exportation. 
All  which  is  performed  by  the  force  of  the  water, 
without  the  aid  of  manual  labour,  except  to  set 
the  different  machines  in  motion,  ^c.  Which  les- 
sens the  labour  and  expense  of  attendance  of 
flour  mills,  fully  one-half  See  the  whole  applied, 
plate  VIII. 


Xo 


THE 

YOUNG  MILL-WRIGHT'S 
GUIDE. 


PART  THE  THIRD. 


CHAPTER  L 

DESCRIPTION  OF  MACHINES. 


ART.    88. 

1.  Of  the  Elevator. 

THE  elevator  is  an  endless  strap,  revolving  over 
two  pullies,  one  of  which  is  set  where  the  grain  or  meal, 
&c.  is  to  be  hoisted  from,  and  the  other  where  it  is  to  be 
hoisted  to  ;  to  this  strap  is  fastened  a  number  of  small 
buckets,  which  fill  themselves  as  they  pass  under  the 
lower  pulley,  and  empty  as  they  pass  over  the  upper 
one.  To  prevent  waste  of  what  may  spill  out  of  these 
buckets,  the  strap,  buckets  and  pullies,  are  all  enclosed, 
and  work  in  tight  cases ;  so  that  what  spills  will  descend 
to  the  place  from  whence  it  was  hoisted.  A  B,  in  fig.  1, 
plate  VI,  is  an  elevator  for  raising  grain,  which  is  let  in 
at  A,  and  discharged  at  B  into  the  spouts  leading  to  the 
different  gamers.  Fig.  S  is  a  perspective  of  the  strap  and 
different  kinds  of  buckets,  and  the  various  modes  of 
fastening  them  to  the  strap. 

S.  Of  the  Conveyer. 

The  conveyer  K  I,  plate  VI,  fig.  1,  is  an  endless  screw 
of  two  continued  spires,  put  in  motion  in  a  trough  ;  the 

D  d 


21©  DESCRIPTION  OF  MACHINES.  [Chap.  1. 

grain  is  let  in  at  one  end,  and  the  screw  drives  it  to  the 
other,  or  collects  it  to  the  centre,  as  at  y,  to  run  into  the 
elevator,  (see  plate  VIII,  37 — 36 — 1,  and  44 — h5)  or  it  is 
let  in  at  the  middle,  and  conveyed  each  way,  as  15 — 16, 
plate  VIII. 

Plate  VI,  fig.  3,  is  a  top  view  of  the  lower  pulley  of  a 
meal  elevator  in  its  case,  and  a  meal  conveyer  in  its  trough, 
for  conveying  meal  from  the  stones,  as  fast  as  ground,  into 
the  elevator.  This  is  an  8  sided  shaft,  set  on  all  sides 
w'nh  small  inclining  boards,  called  flights,  for  conveying 
the  meal  from  one  end  of  the  trough  to  the  other ;  these 
flights  are  set  in  a  spiral  line,  as  shown  by  the  dotted 
line  ;  but  being  set  across  said  line,  changes  the  princi- 
ple of  the  machine  from  a  screw  to  that  of  ploughs,  which 
is  found  to  answer  better  for  conveying  warm  meal. 

Besides  these  conveying  flights,  half  their  number  of 
others  are  sometimes  necessary  ;  which  are  called  lifters, 
and  set  with  their  broadsides  foremost,  to  raise  the  meal 
from  one  side,  and  let  it  fall  on  the  other  side  of  the 
shaft  to  cool ;  these  are  only  used  where  the  meal  is  hot, 
and  the  conveyer  short.  See  SI — 22,  in  plate  VIII ;  which 
is  a  conveyer,  carrying  the  meal  from  3  pair  of  stones  to 
the  elevator,  23 — 24. 

3.  Of  the  Hopper -hoy. 

Fig.  13,  plate  VII,  is  a  hopper-boy ;  which  consists 
of  a  perpendicular  shaft,  A  B,  put  in  a  slow  m.otion  (not 
above  4  revolutions  in  a  minute)  carrying  round  with  it 
the  horizontal  piece  C  D,  which  is  called  the  arms,  and 
set  on  the  under  side,  full  of  small  inclining  boards,  called 
flights,  so  set  as  to  gather  the  meal  to\vards  the  centre, 
or  spread  it  from  the  centre  to  that  part  of  the  arm  which 
passes  over  the  bolting  hopper;  at  which  part,  one  board 
is  set  broadside  foremost,  as  E,  (called  the  sweeper)  which 
drives  the  meal  before  it,  and  drops  it  into  the  hoppers 
H  H,  as  the  arms  pass  over  them.  The  meal  is  generally 
let  fall  from  the  elevator,  at  the  extremity  of  the  arm,  at 
D,  where  there  is  a  sa\  eeper,  which  drives  the  meal  before 
it,  ti'ailing  it  in  a  circle  the  whole  way  round,  so  as  to  dis- 
charge nearly  the  whole  of  its  load,  by  the  time  it  returns 


6hap.  1.]  DESCRIPTION  OF  MACHINES.  211 

to  be  loaded  again :  the  flights  then  gather  it  towards 
the  centre,  from  every  part  of  the  circle ;  which  would 
not  be  the  case,  if  the  sweepers  did  not  lay  it  round  ; 
but  the  meal  would  be  gathered  from  only  one  side  of 
the  circle.  These  sweepers  are  screwed  on  the  back  of 
the  arm,  so  that  they  may  be  raised  or  lowered,  in  order 
to  make  them  discharge  sooner  or  later,  as  necessary. 

The  extreme  flight  of  each  end  of  the  arms  are  put  on 
with  a  screw  passing  through  its  centre,  so  that  they  may 
be  turned  to  drive  the  meal  outwards ;  the  use  of  which 
is,  to  spread  the  warm  meal  as  it  falls,  from  the  elevator, 
in  a  ring  round  the  hopper- boy,  while  it  at  the  same  time 
gathers  the  cool  meal  into  the  bolting  hopper ;  so  that 
the  cold  meal  may  be  bolted,  and  the  warm  meal  spread 
to  cool,  by  the  same  machine,  at  the  same  time,  if  the 
miller  chooses  so  to  do.  The  foremost  edge  of  the  arms 
is  sloped  up,  in  order  to  make  them  rise  over  the  meal, 
and  its  weight  is  nearly  balanced  by  the  weight  w,  hung 
to  one  end  of  a  cord,  passing  over  the  pulley  P,  and  to 
the  stay  iron  F.  About  4-|  feet  of  the  lower  end  of  the 
upright  shaft  is  made  round,  passing  loosely  through  a 
round  hole  in  the  flight  arm,  giving  it  liberty  to  rise  and 
fall  freely,  to  suit  any  quantity  of  meal  under  it.  The 
flight  arm  is  led  round  by  the  leading  arm  L  M,  by  a 
cord  passing  through  the  holes  L  M,  at  each  end,  and 
made  fast  to  the  flight  arm  D  C.  This  cord  is  lengthen- 
ed or  shortened  by  a  hitch-stick  N,  with  two  holes  for 
the  cord  to  pass  through,  the  end  of  the  cord  being  pass- 
ed through  a  hole  at  D,  and  fastened  to  the  end  of  a 
stick  ;  this  cord  must  reeve  freely  through  the  holes  at 
the  end  of  the  arms,  in  order  that  the  ends  may  both  be 
led  equally.  The  flight  arm  falls  behind  the  leader  about 
1  6th  part  of  the  circle.  The  stay-iron  C  F  E,  is  a  ring 
at  F,  which  fits  the  shaft  loosely,  and  is  for  keeping  the 
arm  steady,  and  hanging  the  ends  of  an  equal  height  by 
the  screws  C  E. 

Plate  VII,  fig.  13,  is  a  perspective  view  of  the  under 
side  of  the  flight  arms.  The  arm  a  c,  with  flights  and 
sweepers  complete;  s  s  s  shews  the  screw^s  which  fasten 
the  sweepers  to  the  arms.  The  arn-  c-b,  is  to  shew  the 
rule  for  laying  out  for  the  flights.    Wnen  the  sweeper  at 


212  DESCRIPTION  OF  MACHINES.  [Chap.  1 

b,  is  turned  in  the  position  of  the  dotted  line,  it  drives 
the  meal  outwards.  Plate  VII,  fig.  14,  is  a  plate  on  the 
bottom  of  the  shaft,  to  keep  the  arm  from  the  floor,  and 
15  is  the  step  gudgeon. 

4.  Of  the  Brill. 

The  drill  is  an  endless  strap  revolving  over  two  pullies, 
like  an  elevator,  but  set  nearly  horizontal,  and  instead  of 
buckets,  there  are  small  rakes  fixed  to  the  strap,  which 
draw  the  grain  or  meal  along  the  bottom  of  the  case. 
See  G  H,  in  plate  VI,  fig.  1.  The  grain  is  let  in  at  H, 
and  discharged  at  G.  This  can  sometimes  be  applied 
with  less  expense  than  a  conveyer  ;  if  it  is  set  a  little 
descending,  it  will  move  grain  or  meal  with  ease,  and  will 
do  well  a  little  ascending. 

5.  Of  the  Descender. 

The  descender  is  a  broad  endless  strap  of  very  thin 
pliant  leather,  canvas,  or  flannel,  &c.  revolving  over  two 
pullies,  which  turn  on  small  pivots,  in  a  case  or  trough, 
to  prevent  waste,  one  end  of  which  is  to  be  lower  than 
the  other.  See  EF,  plate  VI,  fig.  1.  The  grain  or  meal 
falls  from  the  elevator  on  the  upper  strap,  at  E,  and  by  its 
own  gravity  and  fall,  sets  the  machine  in  motion,  and  it 
discharges  the  load  over  the  lower  pulley  F.  There  are 
two  small  buckets  to  bring  up  what  may  spill  or  fall  off" 
the  strap,  and  lodge  in  the  bottom  of  the  case. 

This  machine  moves  on  the  principles  of  an  overshot 
water-wheel,  and  will  convey  meal  a  considerable  dis- 
tance, with  a  small  descent.  Where  a  motion  is  easily 
obtained  from  the  water,  it  is  to  be  preferred  to  that  of 
working  itself,  it  being  easily  stopped,  is  apt  to  be  trou- 
blesome. 

The  crane  spout  is  hung  on  a  shaft  to  turn  on  pivots 
or  a  pin,  so  that  it  may  turn  every  way  like  a  crane  ;  into 
this  spout  the  grain  falls  from  the  elevator,  and,  by  turn- 
ing, it  can  be  directed  into  any  garner.  The  spout  is  made 
to  fit  close,  and  play  under  a  broad  board,  and  the  grain  is 
let  into  it  through  the  middle  of  this  board,  near  the  pin, 
so  that  it  will  always  enter  the  spout.  See  it  under  B,  plate 
VI,  fig.  1.  L  is  a  view  of  the  under  side  of  it,  and  M  is  a  top 
view  of  it.  The  pin  or  shaft  may  reach  down  so  low,  that 
a  man  may  stand  on  the  floor  and  turn  it  by  the  handle  x. 


Chap.2.]      APPLICATION  OF  MACHINES. 


2% 


CHAPTER  II. 

ART.    89. 

APPLICATION  OF  THE  MACHINES,  IN  THE  PROCESS  OF  MANU- 
FACTURING WHEAT  INTO  SUPERFINE  FLOUR. 

PLATE  VIII,  is  not  meant  to  shew  the  plan  of  a 
mill ;  but  merely  the  application  and  use  of  the  patented 
machines. 

The  grain  is  emptied  from  the  wagon  into  the  spout 

1,  which  is  set  in  the  wall,  and  conveys  it  into  the  scale 

2,  that  is  made  to  hold  10,  20,  30,  or  60  bushels,  at  plea- 
sure. 

There  should,  for  the  convenience  of  counting,  be 
weights  of  601bs.  each;  divided  into  30,  15,  and  7|lbs. 
then  each  weight  would  show  a  bushel  of  wheat,  and 
the  smaller  ones  halves,  pecks,  &c.  which  any  one  could 
count  with  ease. 

When  the  wheat  is  weighed,  draw  the  gate  at  the  bot- 
tom of  the  scale,  and  let  it  run  into  the  garner  3 ;  at  the 
bottom  of  ^\hich  there  is  a  gate  to  let  it  into  the  elevator 
4 — 5,  which  raises  it  to  5,  and  the  crane  spout  being 
turned  over  the  great  store  gamer  6,  which  communi- 
cates from  floor  to  floor,  to  garner  7,  over  the  stones  8, 
which  suppose  to  be  for  shelling  or  rubbing  the  wheat, 
before  it  is  ground,  to  take  off"  all  dust  that  sticks  to  the 
grain,  to  break  smut  or  fly-et^en  grain,  lumps  of  dust, 
&c.  As  it  is  rubbed  it  runs,  b}-  the  dotted  lines,  into  3 
again ;  in  its  passage  it  goes  throwh  a  current  of  \vind 
blowing  into  the  tight  room  9,  having  only  the  spout  a, 
through  the  lower  floor,  for  the  wind  to  tsicape ;  all  the 
chafi"  will  settle  in  the  room,  but  most  of  the  dust  passes 
out  with  the  wind  at  a.  The  ^heat  again  runs  into  the 
elevator  at  4,  and  the  crane  spout,  at  5,  is  turned  over 
die  screen  hoppers  10  or  11,  and  the  grain  lodged  there, 
out  of  which  it  runs  into  the  rolling  screen  12,  and  de- 
scends through  the  current  of  wind  made  by  the  fan  13 ; 
the  clean  heavy  grain  descends,  by  14,  into  the  conveyer 
15 — 16,  which  conveys  it  into  all  the  garners  over  the 


214  APPLICATION  OF  MACHINES.       [Chap.e. 

stones  7 — 17 — 18,  and  these  regularly  supply  the  stones 
8 — 19 — 30,  keeping  always  an  equal  quantity  in  the  hop- 
pers, which  will  cause  them  to  feed  regularly;  as  it  is 
ground  the  meal  falls  to  the  conveyer  21 — 22,  which 
collects  it  to  the  meal  elevator,  at  23,  and  it  is  raised  to 
24,  whence  it  gently  runs  down  the  spout  to  the  hopper- 
boy  at  25,  which  spreads  and  cools  it  sufficiently,  and 
gathers  it  into  the  bolting  hoppers,  both  of  which  it  at- 
tends regularly ;  as  it  passes  through  the  superfine  cloths 
26,  the  superfine  flour  falls  into  the  packing  chest  28, 
which  is  on  the  second  floor.  If  the  flour  is  to  be  loaded 
on  wagons,  it  should  be  packed  on  this  floor,  that  it 
may  conveniently  be  rolled  into  them ;  but  if  the  flour  is 
to  be  put  on  board  a  vessel,  it  will  be  more  convenient 
to  pack  on  the  lower  floor,  out  of  chest  29,  and  roll  it 
into  the  vessel  at  30.  The  shorts  and  bran  should  be 
kept  on  the  second  floor,  that  they  may  be  conveyed  by 
spouts  into  the  vessel's  hold,  to  save  labour. 

The  rublings  which  fall  from  the  tail  of  the  1st  reel 
28,  are  guided  into  tlie  head  of  the  2d  reel  27;  which  is 
in  the  same  chest,  near  the  floor,  to  save  both  room  and 
machinery.  On  the  head  of  this  reel  is  6  or  7  feet  of  fine 
cloth,  for  tail  flour,  and  next  to  it  the  middling  stuff",  &c. 

The  tail  flour  which  falls  from  the  tail  of  the  1st  reel 
26,  and  head  of  the  2d  reel  37;  and  requires  to  be  bolt- 
ed over  again,  is  guided  by  a  spout,  as  shown  by  dotted 
lines  21—^23,  into  the  conveyer  33 — 33,  to  be  hoisted 
again  with  the  ground  mea^?  a  litde  bran  may  be  let  in 
with  it,  to  keep  the  cloth  open  in  warm  weather — But  if 
there  be  not  a  fall  si'^cient  for  the  tail  flour  to  run  into 
the  lower  conveyer,  there  may  be  one  set  to  convey  it 
into  the  elevatoi,  as  31 — 33.  There  is  a  little  regulating 
board,  turning  on  the  joint  x  under  the  tail  of  the  first  reels, 
to  guide  more  or  less  with  the  tail  flour. 

TJie  middlings,  as  they  fall,  are  conveyed  into  the  eye 
of  either  pair  of  mill-stones  by  the  conveyer  31 — 33, 
and  ground  over  with  the  wheat;  which  is  the  best  way 
of  grinding  them,  because  the  grain  keeps  them  from 
being  killed,  and  there  is  no  time  lost  in  doing  it,  and 
they  are  regularly  mixed  with  the  flour.  There  is  a 
slanting  sliding  board,  to  guide  the  middlings  over  the 


Chap.2.]      APPLICATION  OF  MACHINES.  215 

conveyer,  that  the  miller  may  take  only  such  part,  for 
grinding  over,  as  he  shall  judge  fit:  and  a  little  regulat- 
ing board  between  the  tail  flour  and  middlings,  to  guide 
more  or  less  into  the  stones  or  elevator. 

The  light  grains  of  wheat,  screenings,  &c.  after  being 
blown  by  the  fan  13,  fall  into  the  screenings  garner  32; 
the  chaff"  is  driven  further  on,  and  settles  in  the  chaff'-room 
33 ;  the  greater  part  of  the  dust  will  be  carried  out  with 
the  wind  through  the  wall.  For  the  theory  of  fanning 
wheat,  see  art.  83.* 

To  clean  the  Screenings. 

Draw  the  little  gate  34,  and  let  them  into  the  eleva- 
tor at  4,  and  be  elevated  into  garner  10;  then  draw  gate 
10,  and  shut  11  and  34,  and  let  them  pass  through  the 
rolling  screen  12  and  fan  13,  and  as  they  fall  at  14,  guide 
them  down  a  spout  (shown  by  dotted  lines)  into  the 
elevator  at  4,  and  elevate  them  into  the  screen-hopper 
11;  then  draw  gate  11,  shut  10,  and  let  them  take  tKe 
same  course  over  again,  and  return  into  garner  10,  &c. 
as  often  as  necessary,  and,  when  cleaned,  guide  them 
into  the  stones  to  be  ground. 

The  screenings  of  the  screenings  are  now  in  gamer 
32,  \\  hich  may  be  cleaned  as  before,  and  an  inferior  qua- 
lity of  meal  made  out  of  them. 

By  these  means  the  wheat  may  be  effectually  sepa- 
rated from  the  seed  of  weeds,  &c.  saved  for  food  for 
cattle. 

This  completes  the  w^hole  process  from  the  wagon 
to  the  wagon  again,  without  manual  labour,  except  in 
packing  the  flour,  and  rolling  it  in. 


•  The  boUinjj-reels  m'cy  all  be  set  in  a  line  connected  by  joint  gudgeons, 
supported  by  bearers.  The  meal,  as  it  leaves  the  tail  of  one  reel,  may  be 
intioduced  into  the  head  of  tlie  other,  by  an  elevator  bucket  fixed  on  th* 
head  of  the  reel  open  at  ihe  side  next  the  centrt,  so  that  it  will  dip  up  the 
njeal,  arid  as  it  passes  over  the  centre  drop  in-  This  improvement  was  made 
by  Mr.  Jonathan  Ellicott,  and  by  it  in  many  cases  manj  wheels  and  shafts^ 
and  much  room  may  be  saved,  and  suit  the  convenience  of  the  house,  &c» 


2m         APPLICATION  OF  MACHINES.        [Chap.2. 

ARTICLE    90. 
OF  ELEVATING  GRAIN  FROM  SHIPS. 

If  the  wheat  comes  to  the  mill  by  ships.  No.  35,  aiid 
requires  to  be  measured  at  the  mill,  then  a  conveyer, 
35 — 4,  may  be  set  in  motion  by  the  great  cog-wheel, 
and  may  be  under  or  above  the  lower  floor,  as  may  best 
suit  the  height  of  the  floor  above  high  water.  This  con- 
veyer must  have  a  joint,  as  36,  in  the  middle,  to  give 
the  end  that  lays  on  the  side  of  the  ship,  liberty  to  raise 
and  lower  with  the  tide.  The  wheat,  as  measured,  is 
poured  into  the  hopper  at  35,  and  is  conveyed  into  the 
elevator  at  4;  which  conveyer  will  so  rub  the  grain  as 
to  answer  the  end  of  rubbing  stones.  And,  in  order  to 
blow  away  the  dust,  when  rubbed  off",  before  it  enters 
the  elevator,  part  of  the  wind  made  by  the  fan  13,  may 
be  brought  down  by  a  spout,  13 — 36,  and,  when  it 
enters  the  case  of  the  conveyer,  will  pass  each  way,  and 
blow  out  the  dust  at  37  and  4. 

In  some  instances,  a  short  elevator,  with  the  centre  of 
the  upper  pulley,  38,  fixed  immoveable,  the  other  end 
standing  on  the  deck,  so  much  aslant  as  to  give  the  ves- 
sel liberty  to  raise  and  lower,  the  elevator  sliding  a  little 
on  the  deck.  The  case  of  the  lower  strap  of  this  eleva- 
tor must  be  considerably  crooked,  to  prevent  the  points 
of  the  buckets  from  wearing  by  rubbing  the  descent. 
The  wheat,  as  measured,  is  poured  into  a  hopper,  which 
lets  it  in  at  the  bottom  of  the  pulley. 

But  if  the  grain  is  not  to  be  measured  at  the  mill,  then 
fix  the  elevator  35 — 39,  to  take  it  out  of  the  hole,  and 
elevate  it  into  any  door  convenient.  The  upper  pulley 
is  fixed  in  a  gate  that  plays  up  and  down  in  circular  rab- 
bits, to  raise  and  lower  to  suit  the  tide  and  depth  of  the 
hole  to  the  wheat.  40  is  a  draft  of  the  gate  and  manner 
of  hanging  the  elevator  in  it.  See  a  particular  descrip- 
tion in  the  latter  part  of  art.  95. 

This  gate  is  hung  by  a  strong  rope  passing  over  a 
strong  pulley  or  roller  41,  and  thence  round  the  axis  of 
the  wheel  42:  round  the  rim  of  which  wheel  there  is  a 
rope,  which  passes  round  the  axis  of  wheel  'IS,  round 


Chap.  2.]      APPLICATION  OF  MACHINES.        £17 

the  rim  of  which  is  a  small  rope,  leading  down  over  the 
pulley  P,  to  the  deck,  and  fastened  to  the  cleet  q ;  a  man 
by  pulling  this  rope  can  hoist  the  whole  elevator ;  be- 
cause if  the  diameter  of  the  axis  be  1  foot,  and  the  wheel 
4  feet,  the  power  is  increased  16  fold,  by  art.  20.  The 
elevator  is  hoisted  up,  and  rested  against  the  wall,  until 
the  ship  comes  to,  and  is  fastened  steady  in  the  right 
place,  then  it  is  set  in  the  hold  on  the  top  of  the  wheat, 
and  the  bottom  being  open,  the  buckets  fill  as  tliey  pass 
under  the  pulley;  a  man  holds  by  the  cord,  and  lets  the 
elevator  settle  as  the  wheat  sinks  in  the  hold,  until  the 
lower  part  of  the  case  rests  on  the  bottom  of  the  hold, 
it  being  so  long  as  to  keep  the  buckets  from  touching 
the  vessel ;  by  this  time  it  will  have  hoisted  1,  2,  or  300 
bushels,  according  to  the  size  of  the  ship  and  depth  of 
the  hold,  at  the  rate  of  300  bushels  per  hour.  When 
the  grain  ceases  running  in  of  itself,  the  man  may  shovel 
it  up,  till  the  load  is  discharged. 

The  elevator  discharges  the  wheat  into  the  conveyer 
at  44,  which  conveys  it  into  the  screen-hoppers  10 — 11, 
or  into  any  other,  from  which  it  may  descend  into  the 
elevator  4—5,  or  into  the  rubbing-stones  8. 

This  conveyer  may  serve  instead  of  rubbing-stones, 
and  the  dust  rubbed  off  thereby  may  be,  by  a  wind- 
spout  from  the  fan  13,  into  the  conveyer  at  45,  blown 
out  through  the  wall  at  p.  The  holes  at  44  and  10 — 11 
are  to  be  small,  to  let  but  little  wind  escape  any  where 
but  out  through  the  wall,  where  it  will  carry  the  dust. 

A  small  quantity  of  wind  might  be  let  into  the  con- 
veyer 15 — 16,  to  blow  away  the  dust  rubbed  off  by  it. 

The  fan  must  be  made  to  blow  very  strong,  to  be  suffi- 
cient for  all  these  purposes,  and  the  strength  of  the  bbst 
regulated  as  directed  by  art.  83. 


ART.    91. 
A  MILL  FOR  GRINDING  PARCELS.         ^ 

Here  each  person's  parcel  is  to  be  stored  in  a  separate 
garner,  and  kept  separate  through  the  whole  process  of 

Ee 


t^?l\ 


>/.-» 


218         APPLICATION  OF  MACHINES.      [Chap.  a. 

imaniifacture,  w  hich  occasions  much  labour ;  almost  all 
of  which  is  performed  by  the  machines.  See  plate  VI. 
fig.  I ;  which  is  a  view  of  one  side  of  a  mill  containing  a 
number  of  garners  holding  parcels,  and  a  side  view  of 
the  wheat  elevator. 

The  grain  is  emptied  into  the  garner  g,  from  the  wa- 
gon, as  shewn  in   Plate  VIII ;  and  by  drawing  the  gate 

A,  it  is  let  into  the  elevator  AB,  and  elevated  into  the 
crane-spout  B,  which  being  turned  into  the  mouth  of 
the  garner-spout  BC,  which  leads  over  the  top  of  a  num- 
ber of  garners,  and  has,  in  its  bottom,  a  litde  gate  over 
each  garner  ;  w  hich  gates  and  garners  are  all  numbered 
with  the  same  numbers  respectively. 

Suppose  we  wish  to  deposit  the  grain  in  the  garner 
No.  2,  draw  the  gate  3  out  of  the  bottom,  and  shut  it  in 
the  spout,  to  stop  the  wheat  from  passing  along  the  spout 
past  the  hole,  so  that  it  must  all  fall  into  the  garner ; 
and  thus  for  the  other  garners  3-4-5-6,  &c.  These  gar- 
ners are  all  made  like  hoppers,  about  4  inches  wide  at 
the  floor,  and  nearly  the  length  of  the  garner ;  but  as  it 
passes  through  the  next  story,  it  is  brought  to  the  form 
of  a  spout  4  inches  square,  leading  down  to  the  general 
spout  KA,  which  leads  to  the  elevator  ;  in  each  of  these 
spouts  is  a  gate  numbered  with  the  number  of  its  garner; 
so  that  when  we  want  to  grind  the  parcel  in  gamer  2,  we 
draw  the  gate  2  in  the  lower  spout,  to  let  the  wheat  run 
into  the  elevator  at  A,  to  be  elevated  into  the  crane-spout 

B,  v^hich  is  to  be  turned  over  the  rolling-screen,  as  shewn 
in  Plate  VIII. 

Under  the  upper  tier  of  garners,  there  is  another  tier 
in  the  next  story,  set  so  that  the  spouts  from  the  bottom 
of  the  upper  tier  pass  down  the  partitions  of  the  lower 
tier,  and  the  upper  spouts  of  the  lower  tier  pass  between 
the  partitions  of  the  upper  tier,  to  the  garner-spout. 

These  garners,  and  the  gates  leading  both  into  and 
out  of  them,  are  numbered  as  the  others. 

If  it  is  not  convenient  to  fix  the  descending  spouts 
BC,  to  convey  the  wheat  from  the  elevator  to  the  gar- 
ners, and  KA  to  convey  it  from  the  garners  to  the  eleva- 
tor again,  then  the  conveyers  r-s  and  I-K  may  be  used 
for  said  purposes. 


Chap.2.]       APPLICATION  OF  MACHINES.  219 

To  keep  the  parcels  separate,  there  should  be  a 
crane- spout  to  the  meal  elevator,  or  any  other  method, 
by  which  the  meal  of  tlie  second  parcel  may  be  guided 
to  fall  on  another  part  of  the  floor,  until  the  first  parcel  is 
all  bolted,  and  the  chests  cleared  out,  when  the  meal  of 
the  second  parcel  may  be  guided  into  the  hopper-boy. 

I  must  here  observe,  that  in  mills  for  grinding  par- 
cels, the  tail  flour  must  be  hoisted  by  a  separate  elevator 
to  the  hopper-boy,  to  be  bolted  over,  and  not  run  into 
the  conveyer,  as  shewn  in  plate  VIII;  because  then  the 
parcels  could  not  be  kept  separate. 

The  advantages  of  the  machinery,  applied  to  a  mill 
for  grinding  pai'cels,  are  very  great. 

1.  Because  without  them  there  is  much  labour  in 
moving  the  different  parcels  from  place  to  place,  all 
which  is  done  by  the  machinery. 

2.  The  meal,  as  it  is  ground,  is  cooled  by  the  machi- 
nery, in  so  short  a  time,  and  bolted,  that  when  the  grind- 
ing is  done,  the  bolting  is  also  nearly  finished  :  Therefore, 

Ci.  It  saves  room,  because  the  meal  need  not  be 
spread  over  the  floor  to  cool,  there  to  lay  12  hours  as 
usual,  and  none  but  one  parcel  need  be  on  the  floor  at 
once. 

4.  It  gives  greater  despatch,  as  the  mill  need  never 
stop  either  stones  or  bolts,  in  order  to  keep  parcels  sepa- 
rate. The  screenings  of  each  parcel  may  be  cleaned,  as 
directed  in  art.  89,  with  very  little  trouble;  and  the  flour 
may  be  nearly  packed  before  the  grinding  is  finished. 
So  that  if  a  parcel  of  60  bushels  arrive  at  the  mill  in  the 
evening,  the  owner  may  wait  till  morning,  when  he  may 
have  it  all  finished;  he  may  use  the  offal  for  feed  for  his 
team,  and  proceed  with  his  load  to  market. 


ART.    9S. 
A  GRIST  MILL  FOR  GRINDING  VERY  SMALL  PARCELS. 

Fig.  16,  plate  VII,  is  a  representation  of  a  grist-mill, 
so  constructed  that  the  grist  being  put  into  the  hopper,  it 
will  be  ground  and  bolted,  and  return  into  the  bags 
again. 


220         APPLICATION  OF  MACHINES.      [Chap.  2. 

The  grain  is  emptied  into  the  hopper  at  A,  and  as  it 
is  ground  it  runs  into  the  elevator  at  B,  and  is  elevated 
and  let  run  into  the  bolting  hopper  down  a  broad  spout 
at  C,  and,  as  bolted,  it  falls  into  the  bags  at  d.  The 
chest  is  made  to  come  to  a  point  like  a  funnel,  and  a 
division  made  to  separate  the  fine  and  coarse,  if  wanted, 
and  a  bag  put  under  each  part ;  on  the  top  of  this  division 
is  set  a  regulating  board  on  a  joint,  as  x,  by  which  the 
fine  and  coarse  can  be  regulated  at  pleasure. 

If  the  bran  requires  to  be  ground  over,  (as  it  often  does,) 
it  is  made  to  fall  into  a  box  over  the  hopper,  and  by 
drav.'ing  the  little  gate  b,  it  may  be  let  into  the  hopper  as 
soon  as  the  grain  is  all  ground,  and  as  it  is  bolted  the 
second  time,  it  is  let  run  into  the  bag  by  shutting  the  gate 
b,  and  drawing  the  gate  c. 

If  the  grain  is  put  into  the  hopper  F,  then  as  it  is 
ground  it  falls  into  the  drill,  which  draws  it  into  the 
elevator  at  B,  and  it  ascends  as  before. 

To  keep  the  different  grists  separate — When  the  miller 
sees  the  first  grist  fall  into  the  elevator,  he  shuts  the  gate 
B  or  d,  and  gives  time  for  it  to  get  all  into  the  bolting 
reel ;  he  then  stops  the  knocking  of  the  shoe  by  pulling 
the  shoe  line,  which  hangs  over  the  pullies  pp,  from  the 
shoe  to  near  his  hand,  making  it  fast  to  a  peg;  he  then 
draws  the  gate  B  or  d,  and  lets  the  second  grist  into  the 
ielevator,  to  fall  into  the  shoe  or  bolting  hopper,  giving 
time  for  the  first  grist  to  be  all  into  the  bags,  and  the 
bags  of  the  second  grist  put  in  their  places ;  he  then  un- 
hitches the  line  from  the  peg,  and  lets  the  shoe  knock 
again,  and  begins  to  bolt  the  second  grist. 

If  he  does  not  choose  to  let  the  meal  run  immediately 
into  the  bags,  he  may  have  a  box  made  with  feet  to  stand 
in  the  place  of  the  bags,  for  the  meal  to  fall  in,  out  of 
which  it  may  be  taken,  and  put  into  the  bags,  by  the 
miller  or  the  owner,  as  fast  as  it  is  bolted,  and  mixed  as 
desired;  and  as  soon  as  the  first  parcel  is  bolted,  the 
little  gates  at  the  mouth  of  the  bags  may  be  shut,  while 
the  meal  is  filled  out  of  the  box,  and  the  second  grist 
may  be  bolting. 

The  advantages  of  this  improvement  on  a  grist-mill 
are, 


Chap.  2.]  APPLICATION  OF  MACHINES.  221 

1.  It  saves  the  labour  of  hoisting,  spreading,  and  cool- 
ing the  meal,  and  caiTying  up  the  bran  to  be  ground 
over,  sweeping  the  chest,  and  filling  up  the  bags. 

2.  It  does  all  with  greater  despatch,  and  less  waste, 
without  having  to  stop  the  stones  or  bolting-reel,  to  keep 
the  grists  separate,  and  the  bolting  is  finished  almost  as 
soon  as  the  grinding ;  therefore  the  owner  will  be  the 
less  time  detained. 

The  chests  and  spouts  should  be  made  steep  to  pre- 
vent the  meal  from  lodging  in  them,  so  that  the  miller, 
by  striking  the  bottom  of  the  chest,  will  shake  out  all 
the  meal. 

The  elevator  and  drill  should  be  so  made  as  to  clean 
out  at  one  revolution.  The  drill  might  have  a  brush  or 
two,  instead  of  rakes,  which  would  sweep  the  case  clean 
at  a  revolution  ;  and  the  shoe  of  the  bolting  hopper  should 
be  short  and  steep,  so  that  it  will  clean  out  soon. 

The  same  machinery  may  be  used  for  merchant- 
work,  by  having  a  crane-spout  at  C,  or  a  small  gate,  to 
turn  the  meal  into  the  hopper-boy  that  tends  the  mer- 
chant bolt. 

A  mill  thus  constructed,  might  grind  grists  in  the  day- 
time, and  merchant- work  at  night. 

A  drill  is  preferable  to  a  conveyer  for  grist-mills,  be- 
cause they  will  clean  out  much  sooner  and  better.  The 
low  er  pulley  of  the  elevator  is  twice  as  large  in  diameter 
as  the  pullies  of  the  drill ;  the  lower  pulley  of  the  elevator, 
and  one  pulley  of  the  drill,  are  on  the  same  shaft,  close 
together,  the  elevator  moves  the  drill,  and  the  pulley  of  the 
drill  being  smallest,  gives  room  for  the  meal  to  fall  into 
the  buckets  of  the  elevator. 


ART.    93. 

OF  ELEVATING  GRAIN,  SALT,  OR  ANYGRANULOUS  SUBSTANCE, 
!•  ROM  SHIPS  INTO  STOREHOUSES,  BY  THE  STRENGTH  OF  A 
HORSE. 

Plate  VII,  fig.  17,  represents  the  elevator,  and  the 
manner  of  giving  it  motion ;  the  horse  is  hitched  to  the 
end  of  the  sweep-beam  A,  by  which  he  turns  the  upright 


222  APPLICATION  OF  HACHINES.  [Chap.  2. 

shaft,  on  the  top  of  which  is  the  driving  cog-wheel,  of  96 
cogs,  2i  inches  pitch,  to  gear  into  the  leading  wheel  of 
20  cogs,  on  the  same  shaft  with  which  is  another  driving 
wheel  of  40  cogs,  to  gear  into  another  leading  wheel  of 
19  cogs,  which  is  on  the  same  shaft  with  the  elevator 
pulley  ;  then  if  the  horse  makes  about  3  revolutions  in 
a  minute  (which  he  will  do  if  he  walk  in  a  circle  of  20 
feet  diameter)  the  elevator  pulley  will  make  about  30 
revolutions  in  a  minute ;  and  if  the  pulley  is  2  feet  in 
diameter,  and  a  bucket  be  put  on  every  foot  of  the  strap, 
to  hold  a  quart  each,  the  elevator  will  hoist  about  187 
quarts  per  minute,  or  320  bushels  in  an  hour,  3840 
bushels  in  12  hours;  and  for  every  foot  the  elevator  is 
high,  the  horse  will  have  to  sustain  the  weight  of  a  quart 
of  wheat ;  say  48  feet,  which  is  the  height  of  the  high- 
est store  houses,  then  the  horse  would  have  to  move  1| 
bushels  of  wheat  upwards,  with  a  velocity  equal  to  his 
own  walk;  which  I  presume  he  can  do  with  ease,  and 
overcome  the  friction  of  the  machinery:  By  which  will 
appear  the  great  advantages  of  this  application. 

The  lower  end  of  the  elevator  should  stand  near  the 
side  of  the  ship,  and  the  grain,  salt,  &c.  &c.  be  emptied 
into  a  hopper  ;  the  upper  end  may  pass  through  a  door 
or  window,  as  may  be  most  convenient ;  the  lower  case 
should  be  a  little  crooked  to  prevent  the  buckets  from 
rubbing  in  their  descent. 


ART.    94. 

OF  AN  ELEVATOR  APPLIED  TO  ELEVATE  GRAIN,  &c.  WROUGHT 
BY  A  MAN, 

Plate  VII,  fig.  18,  AB,  are  two  ratchet  wheels,  with  two 
deep  grooves  in  each  of  them,  for  ropes  to  run  in ;  they 
are  fixed  close  together,  on  the  same  shaft  with  the  upper 
pulley  of  the  elevator,  so  that  they  will  turn  easily  on  the 
shaft  the  backward  way,  but  a  click  falls  into  the  ratchet, 
and  prevents  them  from  turning  forwards.  Fig.  19,  is  a 
side  view  of  the  wheel,  ratchet,  and  click.     C  D  are  two 


Chap.2.]       APPLICATION  OF  MACHINES.  223 

levers,  like  weavers'  treadles,  and  from  lever  C  there  is  a 
li^ht  staff  passes  to  the  foreside  of  the  groove  wheel  B, 
and  made  fast  by  a  rope  half  way  round  the  wheel ;  and 
from  said  lever  C  there  is  a  rope  passing  to  the  backside 
of  the  wheel  A  ;  and  from  lev  er  D  there  is  a  light  staff 
passing  to  the  foreside  of  the  groove  wheel  A,  and  a  rope 
to  the  backside  of  the  groove  wheel  B. 

The  man,  who  is  to  work  this  machine,  stands  on  the 
treadles,  and  holds  by  the  staffs  with  his  hands  :  and  as 
he  treads  on  D  it  descends,  and  the  staff  pulls  forward 
the  wheel  A,  and  the  rope  pulls  backwards  the  wheel 
B,  and  as  he  treads  on  C  the  staff  pulls  forward  the  wheel 
B,  and  the  rope  pulls  backward  the  wheel  A  :  but  as 
the  click  falls  into  the  ratchet,  so  that  the  wheels  cannot 
move  forward  without  turning  the  elevator  pulley,  thus 
it  is  moved  one  way  by  the  treadles ;  and  in  order  to 
keep  up  a  regular  motion,  F  is  a  heavy  fly-wheel,  which 
should  be  of  cast  metal,  to  prevent  much  obstruction 
from  the  air. 

To  calculate  what  quantity  a  man  can  raise  to  any 
height,  let  us  suppose  his  weight  to  be  15()lbs.  which  is 
the  power  to  be  applied,  and  suppose  he  is  able  to  walk 
about  70  feet  up  stairs  in  a  minute,  by  the  strength  of 
both  his  legs  and  arms,  or  which  is  the  same  thing,  to 
move  his  weight  on  the  treadles  70  steps  in  a  minute ; 
then  suppose  we  allow,  as  by  art.  29 — 42,  to  lose  1-3  of 
the  power  to  gain  velocity  and  overcome  friction,  (which 
will  be  a  great  plenty  in  this  case,  because  in  the  experi- 
ment in  the  table  in  art.  37,  when  71bs.  were  charged 
with  6lbs.  they  moved  with  a  velocity  of  2  feet  in  half 
a  second,)  then  there  will  remain  lOOlbs.  raised  70  feet 
in  a  minute,  equal  to  SOOlbs.  raised  35  feet  to  the  top  of 
the  third  story  per  minute,  equal  to  200  bushels  per  hour, 
2400  bushels  in  12  hours. 

The  great  advantages  of  this  application  of  the  eleva- 
tor, and  of  this  mode  of  applying  man's  strength,  will 
apjiear  from  these  considerations,  viz.  he  uses  the 
strength  of  both  his  legs  and  arms,  to  move  his  weight 
only,  from  one  treadle  to  the  other,  which  weight  does 
the  work  ;  whereas,  in  carrying  bags  on  his  back,  he 
uses  the  strength   of  his   legs  only,   to  raise  both  the 


224  APPLICATION  OF  MACHINES.    [Chap.  2. 

weight  of  his  body  and  the  burden,  add  to  this  that  he 
generally  takes  a  very  circuitous  route  to  the  place  where 
he  is  to  empty  the  bag,  and  returns  empty  ;  whereas  the 
elevator  takes  the  shortest  direction  to  the  place  of 
emptying,  and  is  always  steadily  at  work. 

The  man  must  sit  on  a  high  bench,  as  a  weaver  does, 
on  which  he  can  rest  part  of  his  weight,  and  rest  himself 
occasionally,  when  the  machine  moves  lightly,  and  have 
a  beam  above  his  head,  that  he  may  push  his  head 
against,  to  evercome  extraordinary  resistances.  This  is 
probably  the  best  means  of  applying  man's  strength  to 
produce  rotary  motions. 

DESCRIPTION  OF  PLATE  IX, 

The  grain  is  emptied  into  the  spout  A,  by  which  it 
descends  into  the  garner  B ;  whence  by  drawing  the 
gate  at  C,  it  passes  into  the  elevator  C  D,  which  raises 
it  to  D,  and  empties  it  into  the  crane  spout  E,  which  is 
so  fixed  on  gudgeons  that  it  may  be  turned  to  any  sur- 
rounding granaries,  into  the  screen-hopper  F,  for  in- 
stance, (which  has  two  parts  F  and  G,)  out  of  which  it 
is  let  into  the  rolling  screen,  at  H,  by  drawing  the  small 
gate  a.  It  passes  through  the  fan  I,  and  falls  into  the 
little  sliding-hopper  K,  which  may  be  moved,  so  as  to 
guide  it  into  either  of  the  hanging- garners,  over  the 
stones,  L  or  M,  and  it  is  let  into  the  stone-hoppers  by 
the  little  bags  bb,  as  fast  as  it  can  be  ground.  When 
ground  it  falls  into  the  conveyer  N  N,  wliich  carries  it 
into  the  elevator  at  O  O,  this  raises  and  empties  it  into 
the  hopper- boy  at  P,  which  is  so  constructed  as  to  carry 
it  round  in  a  ring,  gathering  it  gradually  towards  the 
centre,  till  it  sweeps  into  the  bolting  hoppers  Q  Q. 

The  tail  flour,  as  it  falls,  is  guided  into  the  elevator, 
to  ascend  with  the  meal,  and,  that  a  proper  quantity 
may  be  elevated,  there  is  a  regulating  board  R,  set  un- 
der the  superfine  cloths,  on  a  joint  x,  so  that  it  will  turn 
towards  the  head  or  tail  of  the  reel,  and  send  more  or  less 
into  the  elevator,  as  may  be  required. 

There  may  be  a  piece  of  coarse  cloth  or  wire  put  on 
the  tails  of  the  superfine  reels,  that  will  let  all  pass 
through  except  the  bran,  which  falls  out  at  the  tail,  and 


Chap.  2.]     APPLICATION  OF  MACHINES.        225 

a  part  of  which  is  guided  into  the  elevator  with  the  tail 
flour,  to  assist  the  bolting  in  warm  weather  ;  the  quantity- 
is  regulated  by  a  small  board  r,  set  on  a  joint  under  the 
"ends  of  the  reels.  Beans  may  be  used  to  keep  the  cloths 
open,  and  still  be  returned  into  the  elevator  to  ascend 
again.  What  passes  through  the  coarse  cloth  or  wire, 
and  the  remainder  of  the  bran,  are  guided  into  the  reel 
S,  to  be  bolted. 

To  clean  Wheat  several  Times. 

Suppose  the  grain  to  be  in  the  screen  hopper  E. 
Draw  the  gate  a ;  shut  the  gate  e ;  move  the  sliding 
hopper  K  over  the  spout  K  c  d  ;  and  let  it  run  into  the 
elevator  to  be  raised  again.  Turn  the  crane  spout  over 
the  empty  hopper  G,  and  the  wheat  will  be  all  deposited 
there  nearly  as  soon  as  it  is  out  of  the  hopper  F.  Then 
draw  the  gate  e,  shut  the  gate  a,  and  turn  the  crane 
spout  over  F  ;  and  so  on  alternately,  as  often  as  neces- 
sary.  When  the  grain  is  sufficiently  cleaned,  slide  the 
hopper  K  over  the  hole  that  leads  into  the  stones. 

The  screenings  fall  into  a  garner,  hopperwise,  to  clean 
them  draw  the  gate  f,  and  let  them  run  into  the  elevator, 
to  be  elevated  into  the  screen  hopper  F.  Then  proceed 
with  them  as  with  the  wheat,  till  sufficiently  clean.  To 
clean  the  fannings,  di*aw  the  litde  gate  h,  and  let  them 
into  the  elevator,  &:c.  as  before. 

Fig.  II.  is  a  perspective  view  of  the  conveyer,  as  it 
lies  in  its  troughs,  at  work ;  and  shows  the  manner  in 
which  it  is  joined  to  the  pullies,  at  each  side  of  the 
elevator. 

Fig.  III.  exhibits  a  view  of  the  pulley  of  the  meal 
elevator,  as  it  is  supported  on  each  side,  with  the  strap 
and  buckets  descending  to  be  filled. 

Fig.  IV.  is  a  perspective  view  of  the  underside  of  the 
arms  of  the  hopper-boy,  with  flights  complete.  The 
dotted  lines  show  the  track  of  the  flights  of  one  arm; 
those  of  the  other  following,  and  tracking  between  them. 
A  A  are  the  sweepers.  These  carry  the  meal  round  in  a 
ring,  trailing  it  regularly  all  the  way,  the  flights  drawing 
it  to  the  centre,  as  already  mentioned.  B  B  are  the 
sweepers  that  drive  it  into  the  bolting  hoppers, 

F  f 


226      CONSTRUCTION  OF  MACHINES.     [Chap.  S. 

FiV.  V.  is  a  perspective  view  of  the  bucket  of  the 
Avheat- elevator ;  and  shows  the  manner  in  which  it  is 
fastened,  by  a  broad  piece  of  leather,  which  passes 
through  and  under  the  elevator-strap,  and  is  nailed  to 
the  sides  with  litde  tacks. 


CHAPTER  III. 

©F  THE  CONSTRUCTION  OF  THE  SEVERAL  MACHINES. 

ART.    95. 

OF  THE  WHEAT  ELEVATOR. 

FIRST  determine  how  many  bushels  it  should  hoist 
in  an  hour,  and  where  it  shall  be  set,  so  as  to  answer  all 
the  following  purposes,  if  possible. 

1.  To  elevate  the  grain  from  a  wagon  or  ship. 

2.  From  the  different  garners  into  which  it  may  be 
stored. 

3.  If  it  be  a  two  story  mill,  to  hoist  the  wheat  from 
the  tail  of  the  fan,  as  it  is  cleaned,  to  a  garner  over  the 
stones. 

4.  To  hoist  the  screenings  to  clean  them  several  times. 

5.  To  hoist  the  wheat  from  a  shelling-mill,  if  there 
be  one. 

One  elevator  may  do  all  this  in  a  mill  rightly  planned, 
and  most  of  it  can  be  done  in  mills  ready  built. 

Then  if  you  wish  it  to  hoist  about  300  bushels  in  an 
hour,  make  the  strap  4|  inches  wide,  of  good,  strong, 
white  harness-leather,  only  one  thickness.  It  must  be 
cut  and  joined  together  in  a  straight  line,  with  the  thick- 
est and  consfiquently  the  thinnest  ends  together,  so  that 
if  they  be  too  thin  they  may  be  lapped  over  and  doubled, 
until  they  are  tliick  enough  singly.  Then,  to  make 
wooden  buckets,  take  the  butt  of  a  willow  or  water- 
birch,  that  will  split  freely,  cut  it  in  bolts  15  inches  long, 
and  rive  and  shave  it  into  staves  5|  inches  wide,  and 
three-eighths  of  an  inch  thick  ;  these  will  make  one 
bucket  each.  Set  a  pair  of  compasses  to  the  width  of 
the  strap,  and  make  the  sides  and  middle  of  the  bucket 
equal  thereto  at  the  mouth,  but  let  the  sides  be  only  two- 


Chap.3.]     CONSTRUCTION  OF  MACHINES.         227 

Ihiifls  of  that  width  at  the  bottom,  Avhich  will  make  it  of 
the  form  of  fig.  9,  plate  6 ;  the  ends  being  cut  a  little 
circular,  to  make  the  buckets  lay  closer  to  the  strap  and 
M'heel.  As  it  passes  over,  make  a  pattern  of  the  form 
of  fig.  9,  to  describe  all  the  rest  by.  This  makes  a  bucket 
of  a  neat  form,  to  hold  about  75  solid  inches,  or  some- 
what more  than  a  quart.  Then  to  make  them  bend  to 
a  square  at  the  corners  e  c,  cut  a  mitre  square  across 
where  they  are  to  bend,  about  2-8  through;  boil  them 
and  bend  them  hot,  taking  a  strip  of  leather  across  them, 
to  hold  them  in  that  form  until  they  get  cold,  and  then 
put  bottoms  to  them  of  the  thin  skirts  of  the  harness 
leather.  These  bottoms  are  to  extend  from  the  lower 
end  to  the  strap  that  binds  it  on.  Then,  to  fasten  them 
on  M  ell  and  with  despatch,  prepare  a  number  of  straps 
1|  inches  wide,  of  the  best  cuttings  of  the  harness  leather, 
wet  them  and  stretch  them  as  hard  as  possible,  which 
reduces,  their  width  to  about  Ih  inches.  Nail  one  of 
these  straps  to  the  side  of  a  bucket,  with  5  or  6  strong 
tacks  that  will  reach  through  the  bucket  and  clinch  inside. 
Then  take  a  1|  inch  chisel,  and  strike  it  through  the 
main  strap  about  a  quarter  of  an  inch  from  each  edge, 
and  put  one  end  of  the  binding-strap  through  the  slits, 
draw  the  bucket  very  closely  to  the  strap,  and  nail  it  on 
the  other  side  of  the  bucket,  which  \^  ill  finish  it.  See  B 
in  fig.  2,  plate  6.  C  is  a  meal-bucket  fastened  in  the 
same  manner,  but  is  bottomed  only  with  leather  at  the 
low-er  end,  the  main  strap  making  the  bottom  side  of  it. 
This  is  the  best  way  I  have  yet  discovered  to  make  wood- 
en buckets.  The  scraps  of  the  harness  leather,  out  of 
which  the  elevator-straps  are  cut,  are  generally  about 
enough  to  complete  the  buckets,  which  works  it  all  up. 

To  make  Sheet- Iron  Buckets. 

Cut  the  sheet  in  the  form  of  fig.  8,  plate  VI.  making 
the  middle  part  c,  and  the  sides  a  and  b  nearly  equal  to 
the  width  of  the  strap,  and  nearly  5\  inches  long,  as  be- 
fore. Bend  them  to  a  right  angle  at  every  dotted  line, 
and  the  bucket  wiil  be  formed,  c  will  be  the  bottom  side 
next  to  the  strap ;  and  the  litde  holes  a  a  and  b  b  will 
meet,  and  must  be  rivetted  to  hold  it  together.     The  two 


228        CONSTRUCTION  OF  MACHINES.    [Chap.3. 

holes  c  are  for  fastening  it  to  the  straps  by  rivets.  The 
part  a  b  is  the  part  that  dips  up  the  wheat,  and  the  point 
being  doubled  back  strengthens  it,  and  tends  to  make  it 
wear  well.  The  bucket  being  completely  formed,  and 
the  rivet-holes  made,  spread  one  out  again,  as  fig.  8,  to 
describe  all  the  rest  by,  and  to  mark  for  the  holes,  which 
will  meet  again  when  folded  up.  They  are  fastened  to 
the  strap  by  two  rivets  with  thin  heads  put  inside  the 
bucket,  and  a  double  burr  of  sheet  iron  put  on  the  under 
side  of  the  strap,  which  fastens  them  on  very  tightly. 
See  A,  plate  VI,  fig.  2.  These  buckets  will  hold  about 
1,3  quarts,  or  88  cubic  inches.  This  is  the  best  way  I 
have  found  to  make  sheet-iron  buckets.  D  is  a  meal- 
bucket  of  sheet-iron,  rivetted  on  by  two  rivets,  with  their 
heads  inside  the  strap;  the  sides  of  the  buckets  are  turned 
a  little  out,  and  holes  made  in  them  for  the  rivets  to  pass 
through.  Fig.  11  is  the  form  of  one  spread  out,  and  the 
dotted  lines  show  where  they  are  bent  to  right  angles  to 
form  them.  The  strap  forms  the  bottom  side  of  these 
buckets. 

Make  the  pulleys  24  inches  diameter,  as  thick  as  the 
strap  is  wide,  and  half  an  inch  higher  in  the  middle  than 
at  the  sides,  to  make  the  strap  keep  on ;  give  them  a 
motion  of  25  revolutions  in  a  minute,  and  put  on  a  sheet- 
iron  bucket  for  every  15  inches;  then  125  buckets  will 
pass  per  minute,  which  will  carry  162  quarts,  and  hoist 
300  bushels  in  an  hour,  and  3600  bushels  in  12  hours. 
If  you  wish  to  hoist  faster,  make  the  strap  wider,  the 
buckets  larger  in  proportion,  and  increase  the  velocity 
of  the  pulley,  but  not  above  35  revolutions  in  a  minute, 
nor  more  buckets  than  one  for  every  12  inches,  other- 
wise they  will  not  empty  well.  A  strap  of  5  inches,  with 
buckets  6  inches  long,  and  of  a  width  and  proportion 
suiting  the  strap  (4^  inches  wide)  will  hold  1,8  quarts 
each;  and  35  revolutions  of  the  pulley  will  pass  175 
buckets,  which  will  carry  315  quarts  in  a  minute,  and 
590  bushels  in  an  hour.  If  the  strap  be  4  inches  wide, 
and  the  wooden  buckets  5  inches  deep,  and  in  propor- 
tion t©  the  strap,  they  will  hold  ,8  of  a  quart :  then,  if 
there  be  one  for  every  15  inches,  and  the  pulley  revolves 
27  revolutions  in  a  minute,  it  will  hoist  200  bushels  in 
arf  hour,  where  tliere  is  a  good  garner  to  empty  the 


Chap.  3.]  CONSTRUCTION  OF  MACHINES.         229 

wheat  into.    This  is  sufficient  for  unloading  wagons,  and 
the  size  they  are  commonly  made. 

Plate  VI,  fig.  6,  represents  the  gudgeon  of  the  lower 
pulley ;  fig.  7,  the  gudgeon  for  the  shaft  on  which  the 
upper  pulley  is  fixed.  Fix  both  the  pulleys  in  their  places, 
but  not  firmly,  so  that  a  line  stretched  from  one  pulley 
to  the  other,  will  cross  the  shafts  or  gudgeons  at  right 
angles.  This  must  always  be  the  case  to  make  the 
sti'aps  w  ork  fairly.  Put  on  the  strap  with  the  buckets ; 
draw  it  tightly  and  buckle  it ;  put  it  in  motion,  and  if  it 
does  not  keep  fairly  on  the  pulleys,  their  position  may 
be  altered  a  little.  Observe  how  much  the  descending 
strap  swags  by  the  weight  of  the  buckets,  and  make  the 
case  round  it  so  crooked,  that  the  points  of  the  buckets 
will  not  rub  in  their  descent,  which  will  cause  them  to 
wear  much  longer  and  work  easier.  The  side  boards 
need  not  be  made  crooked  in  dressing  out,  but  may  be 
bent  sufficiently  by  sawing  them  half  way  or  two-thirds 
through,  beginning  at  the  upper  edge,  holding  the  saw 
very  much  aslant,  the  point  downwards  and  inwards,  so 
that  in  bending  the  parts  will  slip  past  each  other.  The 
upper  case  must  be  nearly  straight ;  for  if  it  be  made 
much  crooked,  the  buckets  will  incline  to  turn  under 
the  strap.  Make  the  cases  3-4  of  an  inch  wider  than  the 
strap  and  buckets  inside,  and  1|  inch  deeper,  that  they 
may  play  freely ;  but  do  not  give  them  room  to  turn 
upside  down.  If  the  strap  and  buckets  be  4  inches, 
then  make  the  si'de  boards  5|,  and  the  top  and  bottom 
boards  6|  inches  wide,  of  inch  boards.  Be  careful  that 
no  shoulders  nor  nail-points  be  left  inside  of  the  cases, 
for  the  buckets  to  catch  in.  Make  the  ends  of  each  case, 
where  the  buckets  enter  as  they  pass  over  the  pulleys, 
a  little  wider  than  the  rest  of  the  case.  Both  the  pulleys 
are  to  be  nicely  cased  round  to  prevent  waste,  not  leav- 
ing room  for  a  grain  to  escape,  continuing  the  case  of 
the  same  width  round  the  top  of  the  upper,  and  bottom 
of  the  lower  pulley  ;  then  if  any  of  the  buckets  should 
ever  get  loose,  and  stand  askew,  they  will  be  kept  right 
by  the  case  ;  whereas,  if  there  were  any  ends  of  boards 
or  shoulders,  they  would  catch  against  them.  See  A  B, 
plate  VI,  fig.  1.     The  bottom  of  the  case  of  the  upper 


230  CONSTRUCTION  OF  MACHINES.  [Chap.  3, 

pulley  must  be  descending,  so  that  what  grain  may  be 
falling  out  of  the  buckets  in  passing  over  the  pulleys, 
may  be  guided  into  the  descending  case.  The  shaft 
passing  through  this  pulley  is  made  round  where  the 
case  fits  to  it :  half  circles  are  cut  out  of  two  boards,  so 
that  they  meet  and  embrace  it  closely.  The  undermost 
board,  where  it  meets  the  shaft,  is  ciphered  off  inside 
next  the  pulley,  to  guide  the  grain  inward.  But  it  is 
full  as  good  a  way  to  have  a  strong  gudgeon  to  pass 
through  the  upper  pulley,  Math  a  tenon  at  one  end,  to 
enter  a  socket,  which  may  be  in  the  shaft,  that  is  to  give 
it  motion.  This  will  best  suit  where  the  shaft  is  short, 
and  has  to  be  moved  to  put  the  elevator  out,  and  in 
gear. 

The  way  that  I  have  generally  cased  the  pulleys  is  as 
follows,  viz.  The  top  board  of  the  upper  strap-case, 
and  the  bottom  board  of  the  lower  strap-case  are  ex- 
tended past  the  lower  pulley  to  rest  on  the  floor ;  and 
the  lower  ends  of  these  boards  are  made  two  inches 
narrower,  as  far  as  the  pulley- case  extends ;  the  side 
board  of  the  pulley  is  nailed,  or  rather  screwed,  to  them 
with  wood  screws.  The  rest  of  the  case  boards  join  to 
the  top  of  the  pulley-case,  both  being  of  one  width. 
The  block  which  the  gudgeons  of  this  pulley  run  in,  are 
screwed  fast  to  the  outside  of  the  case  boards  ;  the  gud- 
geons do  not  pass  quite  through,  but  reach  to  the  bottom 
of  the  hole,  which  keeps  the  pulley  in  its  place. 

The  said  top  and  bottom  boards,  and  also  the  side 
boards  of  the  strap-cases,  are  extended  past  the  upper 
pulley,  and  the  side  boards  of  the  pulley- case  are  screwed 
to  them  ;  but  this  leaves  a  vacancy  between  the  top  of 
the  side  boards  of  the  strap-cases,  and  shoulders  for  the 
buckets  to  catch  against.  This  vacancy  is  to  be  filled  up 
by  a  short  board,  guiding  the  buckets  safely  over  the 
upper  pulley.  The  case  must  be  as  close  to  the  points 
of  the  buckets,  where  they  empty,  as  is  safe,  that  as 
little  as  possible  may  fall  down  again.  There  is  to  be  a 
long  hole  cut  into  the  case  at  B,  for  the  wheat  to  fall 
out  at,  and  a  short  spout  guiding  it  into  the  crane  spout. 
The  top  of  the  short  spout  next  B,  should  be  loosely 
fastened  in  with  a  button,  that  it  may  be  taken  off,  to 


Chap.  3.]  CONSTRUCTION  OF  MACHINES.         231 

examine  if  the  buckets  empty  well,  &c.  Some  neat 
workmen  have  a  much  better  way  of  casing  the  pulleys, 
that  I  cannot  here  describe;  what  I  have  described  is 
the  cheapest,  and  does  very  well. 

The  wheat  should  be  let  in  at  the  bottom,  to  meet  the. 
buckets,  and  a  gate  to  shut  as  near  the  point  of  them  as 
possible,  as  at  A,  plate  VI,  fig.  1.  Then  if  the  gate  be 
drawMi  sufficiently  to  fill  the  backets,  and  the  elevator  be 
stopped,  the  wheat  will  stop  running  in,  and  the  eleva- 
tor will  be  free  to  start  again  ;  but  if  it  had  been  let  in 
any  distance  up,  then,  when  the  elevator  stopped,  it 
would  fill  from  the  gate  to  the  bottom  of  the  pulley,  and 
the  elevator  could  not  start  again.  If  it  be  in  any  case 
let  in  any  distance  up,  the  gate  should  be  so  fixed,  that 
it  cannot  be  drawn  so  far,  as  to  let  in  the  wheat  faster 
than  the  buckets  can  take  it,  else  the  case  will  fill  and 
stop  the  buckets.  If  it  be  let  in  faster  at  the  hindmost 
side  of  the  pulley,  than  the  buckets  will  carry  it,  the 
same  evil  will  occur ;  because  the  buckets  will  push  the 
wheat  before  them,  being  more  than  they  can  hold,  and 
give  room  for  too  much  to  come  in  ;  therefore  there 
should  be  a  relief  gate  at  the  bottom  to  let  the  wheat  out, 
if  ever  there  happens  to  get  too  much  in. 

The  motion  is  to  be  given  to  the  upper  pulley  of  all 
elevators,  if  it  can  be  done,  because  the  weight  in  the 
buckets,  causes  the  strap  to  hang  tighter  on  the  upper, 
and  slacker  on  the  lower  pulley  ;  therefore  the  upper 
pulley  will  carry  the  greatest  quantity  without  slipping. 
All  elevators  should  stand  a  little  slanting,  because  they 
will  discharge  the  better.  The  boards  for  the  cases 
should  be  of  any  unequal  lengths,  so  that  two  joints  will 
never  come  close  together,  which  makes  the  case  strong. 
Some  have  joined  the  cases  at  every  floor,  which  is  a 
great  error.  There  must  be  a  door  in  the  ascending 
case,  at  the  most  convenient  place,  to  buckle  the  strap, 
&:c.  &c. 

Of  the  Crane  Spout. 

To  make  a  crane  spout,  fix  a  board  18  or  20  inches 
broad  truly  horizontal,  or  level,  as  a  under  B,  in  plate 
\'l,  fig.  1.     Through  the  middle  of  this  board  the  wheat 


232         CONSTRUCTION  OF  MACHINES.  [Chap.  3. 

is  conveyed,  by  a  short  spout  from  the  elevator.  Then 
make  the  spout  of  4  boards,  12  inches  wide  at  the  up- 
per, and  about  4  or  5  inches  at  the  lower  end.  Cut  the 
upper  end  off  aslant,  so  as  to  fit  nicely  to  the  bottom  of 
the  board ;  hang  it  to  a  strong  pin,  passing  through  the 
broad  board  near  the  hole  through  which  the  wheat 
passes,  so  that  the  spout  may  be  turned  in  any  direction 
and  still  cover  the  ^vhole,  at  the  same  time  it  is  receiving 
the  wheat,  and  guiding  it  into  any  garner,  at  pleasure. 
In  order  that  the  pin  may  have  a  strong  hold  of  the 
board  and  spout,  there  must  be  a  piece  of  scantling,  4 
inches  thick,  nailed  on  the  top  of  the  board,  for  the  pin 
to  pass  through ;  and  another  to  the  bottom,  for  the 
head  of  the  pin  to  rest  on.  But  if  the  spout  be  long  and 
heavy,  it  is  best  to  hang  it  on  a  shaft,  that  may  extend 
down  to  the  floor,  or  below  the  collar-beams,  with  a  pin 
through  it,  as  x,  to  turn  the  spout  by.  In  crane  spouts 
for  meal  it  is  sometimes  best  to  let  the  lower  board 
reach  to,  and  rest  on  the  floor.  If  the  elevator-cases  and 
crane-spout  be  well  fixed,  there  can  neither  grain  nor 
meal  escape  or  be  wasted  that  enters  the  elevator,  until 
it  comes  out  at  the  end  of  the  crane- spout  again. 

Of  an  Elevator  to  elevate  fFheatfrom  a  Ship's  Hbld.^ 

Make  the  elevator  complete  (as  it  appears  '55 — 39, 
plate  8)  on  the  ground  (and  raise  it  afterwards.)  The 
pulleys  are  to  be  both  fixed  in  their  places  and  cased  ; 
and  the  blocks  that  the  gudgeon  of  the  upper  pulley  is 
to  run  in,  are  to  be  rivetted  fast  to  the  case-boards  of  the 
pulley,  and  these  case-boards  screwed  to  the  strap-cases 
by  long  screws,  reaching  through  the  case-boards  edge- 
ways. Both  sides  of  the  pulley-case  are  fastened  by  one 
set  of  screws.  On  the  outside  of  these  blocks,  round 
the  centre  of  the  gudgeons,  are  circular  knobs,  6  inches 
diameter,  and  3  inches  long,  strongly  rivetted  to  keep 
them  from  splitting  off,  because  by  these  knobs  the 
whole  weight  of  the  elevator  is  to  hang.  In  the  move- 
able frame  40.  oo,  oo,  are  these  blocks  with  their  knobs, 
let  into  the  pieces  of  the  frame  B  C  rs.     The  gudgeons 

♦  See  the  description  of  this  elevator  in  art-  90, 


Chap.  3.]     CONSTRUCTION  OF  MACHINES.         !i33 

of  the  upper  pulley  p  pass  through  these  knobs,  and  play 
in  them.  Their  use  is  to  bear  the  weight  of  the  elevator 
that  hangs  by  them  ;  the  gudgeons,  by  this  means,  bear 
only  the  weight  of  the  strap  and  its  load,  as  is  the  case 
with  other  elevators.  Their  being  circular  gives  the 
elevator  liberty  to  swing  out  from  the  wall  to  the  hold  of 
the  ship. 

The  frame  40  is  made  as  follows  :  the  top  piece  A  B 
is  9  by  8,  strongly  tenoned  into  the  side  pieces  A  D 
and  B  C  with  double  tenons,  which  side  pieces  are  8  by 
6.  The  piece  r  s  is  put  in  with  a  tenon,  3  inches  thick, 
which  is  dovetailed,  keyed,  and  drawpinned,  with  an 
iron  pin,  so  that  it  can  easily  be  taken  out.  In  each  side 
piece  A  D  and  B  C  there  is  a  row  of  cogs,  set  in  a  circle, 
that  are  to  play  in  circular  rabbets  in  the  posts  p.  41. 
These  circles  are  to  be  described  with  a  radius,  whose 
length  is  from  the  centre  of  the  joint  gudgeons  G,  to  the 
centre  of  the  pulley  39 ;  and  the  posts  must  be  set  up, 
so  that  the  centre  of  the  circle,  will  be  the  centre  of  the 
gudgeon  G ;  then  the  gears  will  be  always  right,  al- 
though the  elevator  rise  and  fall  to  suit  the  ship  or  tide. 
The  top  of  those  circular  rabbets  ought  to  be  so  fixed, 
that  the  lower  end  of  the  elevator  may  hang  near  the 
wall.  This  may  be  regulated  by  fixing  the  centre  of 
gudgeon  G.  The  length  of  these  rabbets  is  regulated 
by  the  distance  the  vessel  is  to  rise  and  fall,  to  allow  the 
elevator  to  swing  clear  of  the  vessel  light  at  high  water. 
The  best  way  to  make  the  circular  rabbets  is,  to  dress 
two  pieces  of  2  inch  plank  for  each  rabbet,  of  the  right 
circle,  and  pin  them  to  the  posts,  at  such  a  distance, 
leaving  the  rabbet  between  them. 

When  the  gate  and  elevator  are  completed,  and  tried 
together;  the  gate  hung  in  its  rabbets,  and  played  up  and 
down,  then  the  elevator  may  be  raised  by  the  same  pow- 
er ;  that  is,  to  raise  and  lower  it  as  described,  art.  4. 


ART.    96. 

OF  THE  MEAL-ELEVATOR. 

Litde  may  be  said  of  the  manner  of  constructing  the 
meal-elevator,  after  what  has  been  said  in  art.  90,  except 


234        CONSTRUCTION  OF  MACHINES.   [Chap.  3, 

giving  the  dimensions.      Make  the  pulleys  3|  inches 
thick,  and   18  inches  diameter.     Give  them  no  more 
than  SO  revolutions  in  a  minute.     Make  the  strap  3| 
inches    wide,    of  good,    pliant,   white  harness-leather ; 
make  buckets  either  of  wood  or  sheet- iron,  to  hold  about 
half  a  pint  eacli ;  put  one  for  every  foot  of  the  strap ; 
make  the  cases  tight,  especially  round  the  upper  pulley, 
slanting  much  at  bottom,  so  that  the  meal  which  falls 
out  of  the  buckets,  may  be  guided  into  the  descending 
case.      Let  it  lean  a  little,  that  it  may  discharge  the  bet- 
ter.    The  spout  that  conveys  the  meal  from  the  elevator 
to  the  hopper- boy,  should  not  have  much  more  than  45 
degrees  descent,  that  the  meal   may  run  easily  down, 
and  not  cause  a  dust ;  fix  it  so  that  the  meal  will  spread 
thinly  over  its  bottom ;  in  its  descent  it  will  cool  the 
better.     Cover  the  top  of  the  spout  half-way  down,  and 
hang  a  thin,  light  cloth  at  the  end  of  this  cover,  to  check 
all  the  dust  that  may  raise,  by  the  fall  of  the  meal  from 
the  buckets.     Remember  to  take  a  large  cipher  off  the 
inside  of  the  board,  where  it  fits  to  the  undermost  side 
of  the  shaft  of  the  upper  pulley  ;  else  the  meal  will  work 
out  along  the  shaft.     Make  all  tight,  as  directed,  and  it 
will  effectually  prevent  waste. 

In  letting  meal  into  an  elevator,  it  must  be  let  in  some 
distance  above  the  centre  of  the  pulley,  that  it  may  fall 
clear  from  the  spout  that  conveys  it  in  ;  otherwise  it  will 
clog  and  choak.  Plate  VI.  fig.  4,  is  the  double  socket  gud- 
geon of  the  lower  pulley,  to  which  the  conveyer  joins.  Fig. 
3,  a  b  c  d,  is  a  top  view  of  the  case  that  the  pulley  runs 
in,  which  is  constructed  thus  ;  a  b  is  a  strong  plank,  14? 
by  3  inches,  steped  in  the  sill,  dovetailed  and  keyed  in 
the  meal-beam,  and  is  called  the  main  bearer.  In  this, 
at  the  determined  height,  is  framed  the  gudgeoiT^Dearers 
a  c  b  d,  which  are  planks  15  by  l|  inches,  set  Ik  inches 
apart,  the  pulley  running  between,  and  resting  on  them. 
The  end  piece  c  d  7  inches  wide  and  2  thick,  is  set  in 
the  direction  of  the  strap- case,  and  extends  5  inches 
above  the  top  of  the  pulley  ;  to  this  the  bearers  are  nailed. 
On  the  top  of  the  bearers,  above  the  gudgeons,  are  set 
two  other  planks  13  by  i\  inches,  rabbetted  into  the 
main  bearer,  and  screwed  fast  to  the  end  piece  c  d  :  these 


€hap.3.]     CONSTRUCTION  OF  MACHINES.        235 

are  4  inches  above  the  pulley.  The  bottom  piece  of 
this  case  slides  in  between  the  bearers,  resting  on  two 
elects,  so  that  it  can  be  drawn  out  to  empty  the  case, 
if  it  should  ever  by  any  means  be  overcharged  with 
meal;  this  completes  the  case.  In  the  gudgeon  bearer 
under  the  gudgeons  are  mortises,  made  about  12  by  2 
inches,  for  the  meal  to  pass  from  the  conveyer  into  the 
elevator;  the  bottom  board  of  the  conveyer  trough  rests 
on  the  bearer  in  these  mortises.  The  strap-case  joins 
to  the  top  of  the  pulley  case,  but  is  not  made  fast,  but 
the  back  board  of  the  descending  case  is  steped  into  the 
inside  of  the  top  of  the  end  piece  c  d.  The  bottom  of 
the  ascending  case  is  to  be  supported  steady  to  its 
place,  and  the  board  at  the  bottom  must  be  ciphered  off 
at  the  inside,  with  long  and  large  ciphers,  making  them 
at  the  point  only  1-4  inch  thick;  this  is  to  make  tlie  bot- 
tom of  the  case  wide  for  the  buckets  to  enter,  if  any  of 
them  should  be  a  little  askew,  because  the  pulley- case  is 
wider  than  the  strap-cases,  to  give  rooirt  for  the  meal 
from  the  conveyer  to  fall  into  the  buckets ;  and  in  order 
to  keep  the  passage  open,  ihere  is  a  piece  3  inches  wide, 
and  1|  inch  thick,  put  on  each  side  of  the  pulley  to 
stand  at  right  angles  with  each  other,  extending  3| 
inches  at  each  end  past  the  pulley,  and  are  ciphered  off, 
so  as  to  clear  the  strap,  and  draw  the  meal  under  the 
buckets;  these  are  called  bangers. 


ART.    97. 

OF  THE  MEAL.':ONVEYER. 

Sea^t  described,  art.  88.  Plate  VI,  fig.  3,  is  a  conveyer 
joined  to  the  pulley  of  the  elevator.  Fig.  4  is  the  gudgeon 
that  is  put  through  the  lower  pulley,  to  which  the  convey- 
er is  joined  by  a  socket,  as  represented.  Fig.  5  is  a  view 
of  the  said  socket  and  the  band,  as  it  appears  on  the  end 
of  the  shaft.  The  tenon  of  the  gudgeon  is  square,  that 
the  socket  may  fit  it  every  way  alike.  Make  the  shaft 
5|  inches  diameter,  of  eight  equal  sides,  and  put  on  the 
socket  and  the  gudgeon ;  then,  to  lay  it  out  for  the  flights, 


336         CONSTRUCTION  OF  MACHINES.     [Chap.  a. 

begin  at  the  pulley,  mark  as  near  the  end  as  possible, 
on  the  one  side,  and  turning  the  shaft  the  way  it  is  to 
work,  at  the  distance  of  1|  inch  towards  the  other  end, 
set  a  flight  on  the  next  side,  and  thus  go  on  to  mark 
for  a  flight  on  every  side,  still  advancing  1|  inch  to  the 
other  end,  which  will  form  the  dotted  spiral  line,  which 
would  drive  the  meal  the  wrong  way;  but  the  flights 
are  to  be  set  across  this  spiral  line,  at  an  angle  of  about 
30  degrees,  with  a  line  square  across  the  shaft ;  and  then 
they  will  drive  the  meal  the  right  way,  the  flights  operat- 
ing like  ploughs. 

To  make  the  flights,  take  good  maple,  or  other 
smooth  hard  wood;  saw  it  in  6  inch  lengths;  split  it 
always  from  the  sap  to  the  heart;  make  pieces  2|  inches 
wide,  and  3-4  of  an  inch  thick ;  plane  them  smooth  on 
one  side,  and  make  a  pattern  to  describe  them  by,  and 
make  a  tenon  2|  inches  long,  to  suit  a  3-4  inch  auger. 
When  they  are  perfectly  dry,  having  the  shaft  bored, 
and  the  inclination  of  the  flights  marked  by  a  scribe,  drive 
them  in  and  cut  them  oflf  2^  inches  from  the  shaft,  dress 
them  with  their  foremost  edge  sharp,  taking  all  off"  from 
the  back  side,  leaving  the  face  smooth  and  straight,  to 
push  forward  the  meal ;  make  their  ends  nearly  circular. 
If  the  conveyer  be  short,  put  in  lifting  flights,  with  their 
broad  side  foremost,  half  the  number  of  the  others,  be- 
tween the  spires  of  them ;  they  cool  the  meal  by  lifting 
and  letting  it  fall  over  the  shaft. 

To  make  the  trough  for  it  to  run  in,  take  3  boards, 
the  bottom  one  11,  back  15,  and  front  13  inches.  Fix 
the  block  for  the  gudgeon  to  run  in  at  one  end,  and  fill 
the  comers  with  cleets,  to  make  the  bottom  nearly  cir- 
cular, that  but  little  meal  may  lay  in  it ;  join  it  neatly  to 
the  pulley-case,  resting  the  bottom  on  the  bottom  t)f  the 
hole  cut  for  the  meal  to  enter,  and  the  other  end  on  a 
supporter,  that  it  can  be  removed  and  put  to  its  place 
again  with  ease,  without  stopping  the  elevator. 

A  meal-elevator  and  conveyer  thus  made,  of  good 
materials,  will  last  50  years,  with  very  litde  repair,  and 
save  more  meal  from  waste,  than  will  pay  for  building 
and  repairing  them  for  ever.  The  top  of  the  trough 
trjust  be  left  open,  to  let  the  sti'eam   of  the  meal  out : 


.  3.]    CONSTRUCTION  OF  MACHINES.      237 

and  a  door  may  be  made  in  the  ascending  case  of  the 
elevator,  about  4  feet  long,  to  buckle  the  strap  tighter, 
&c.  The  strap  of  the  elevator  turns  the  conveyer,  so 
that  it  will  be  easily  stopped  if  any  thing  should  be 
caught  in  it,  being  dangerous  to  turn  it  by  cogs.  This 
machine  is  often  applied  to  cool  the  meal,  without  the 
hopper-boy,  and  attend  the  bolting-hopper,  by  extend- 
ing it  to  a  great  length,  and  conveying  the  meal  imme- 
diately into  the  hopper,  which  does  very  well,  and  some 
prefer  it ;  but  a  hopper- boy  is  preferable  where  there  is 
room  for  one. 


ART.    98. 
OF  A  GRAIN-CONVEYER. 

This  machine  has  been  constructed  in  a  variety  of 
ways,  the  best  I  take  to  be  as  follows,  viz.  Make  a 
round  shaft,  9  inches  diameter.  Then,  to  make  the 
spire,  take  strong  sheet- iron,  make  a  pattern  3  inches 
broad  and  of  the  true  arch  of  a  circle  ;  the  diameter  of 
which  (being  the  inside  of  the  pattern)  is  to  be  12  inches  ; 
this  will  give  it  room  to  stretch  along  a  9  inch  shaft,  so 
as  to  make  a  hasty  spire,-  that  will  advance  about  21 
inches  along  the  shaft  every  revolution.  By  this  pattern 
cut  the  sheet-iron  into  circular  pieces,  and  join  the  ends 
together  by  rivetting  and  lapping  them,  so  as  to  let  the 
grain  run  freely  over  the  joints  ;  when  they  are  joined 
together  they  will  form  several  circles,  one  above  the 
other,  slip  it  on  the  shaft,  and  stretch  it  along  as  far  as 
you  can,  till  it  comes  tight  to  the  shaft,  and  fasten  it  to 
its  place  by  pins,  set  in  the  shaft  at  the  back  side  of  the 
spire,  and  nail  it  to  the  pins  :  it  will  now  form  a  beauti- 
ful spire  21  inches  apart,  which  is  too  great  a  distance; 
therefore  there  should  be  two  or  three  of  these  spires 
made,  and  wound  into  each  other,  and  all  be  put  on 
together,  because  if  one  be  put  on  first,  the  others  can- 
not be  got  on  so  well  afterwards ;  they  will  then  be  7 
inches  apart,  and  will  convey  wheat  very  fast.  If  these 
spires  be  punched  full  of  holes  like  a  grater,  and  the 


238     CONSTRUCTION  OF  MACHINES.      [Chap.  6. 

trough  lined  with  sheet- iron  punched  full  of  small  holes, 
it  will  be  an  excellent  rubber ;  will  clean  the  wheat  of 
the  dust  and  down,  that  adheres  to  it,  and  supersede  the 
necessity  of  any  other  rubbing-machine. 

The  spires  may  also  be  formed  with  either  wooden 
or  iron  flights,  set  so  near  to  each  other  in  the  spiral 
Hues,  as  to  convey  the  wheat  from  one  to  another. 


ART.    99. 
OP  THE  HOPPER-BOY. 

This  machine  has  appeared  in  various  constructions, 
the  best  of  which  is  represented  by  Plate  VII.  fig.  12 : 
see  the  description,  art.  88. 

To  make  the  flight-arms  C  D,  take  a  piece  of  dry 
poplar,  or  other  soft  scantling  14  feet  long,  8  by  2|  in- 
ches in  the  middle,  5  by  1|  inches  at  the  end,  and 
straight  at  the  bottom ;  on  this  strike  the  middle  line 
a  b,  fig.  13.  Consider  which  way  it  is  to  revolve,  and 
cipher  off"  the  under  side  of  the  foremost  edge  from  the 
middle  line,  leaving  the  edge  3-4  of  an  inch  thick,  as 
appears  by  the  shaded  part.  Then  to  lay  out  the  flights, 
take  the  following 

RULE. 

Set  your  compasses  at  4|  distance,  and,  beginning 
with  one  foot  in  the  centre  c,  step  towards  the  end  b, 
observing  to  lessen  the  distance  one  sixteenth  part  of  an 
inch  every  step ;  this  will  set  the  flights  closer  together 
at  the  end  than  at  the  centre.  Then  to  set  the  flights 
of  one  arm  to  track  truly  between  those  of  the  other,  and 
to  find  their  inclination,  with  one  point  in  the  centre  c, 
sweep  the  dotted  circles  across  every  point  in  one  arm, 
then,  without  altering  the  centre  or  distance,  make  the 
little  dotted  marks  on  the  other  arm,  and  between  them 
the  circles  are  to  be  swept  for  the  flights  in  it.  Then, 
to  vary  their  inclination,  regularly  from  the  end  to  the 
centi-e,  strike  the  dotted  line  c  d  half  an  inch  from  the 
centre  c,  and  2f  inches  from  the  middle  line  at  d.  Then 
with  the  compasses  set  to  half  an  inch,  set  off"  the  incli^ 


Chap.  3.]   CONSTRUCTION  OF  MACHINES.        239 

nation  from  the  dotted  circles  on  the  line  c  d.  Then, 
because  the  line  c  d  approaches  the  middle  line,  the  in- 
clination is  greater  near  the  centre  than  at  the  end,  and 
vary  regularly.  Dovetail  the  flights  into  the  arm,  observ- 
ing to  put  the  side  that  is  to  drive  the  meal  to  the  line  of 
inclination.  The  bottoms  of  them  should  not  extend  past 
the  middle  line,  the  ends  being  all  rounded  and  dressed 
off"  at  the  back  side  to  make  the  point  sharp,  leaving  the 
driving  side  quite  straight  like  the  flight  r.  See  them 
complete  in  the  end  c  a.  The  sweepers  should  be  5  or 
6  inches  long,  screwed  on  behind  the  flights,  at  the 
back  side  of  the  arms,  one  at  each  end  of  the  arm,  and 
one  at  the  part  that  passes  over  the  hopper  :  their  use  is 
described  art.  88. 

The  upright  shaft  should  be  4  by  4  inches,  and  made 
round  for  about  4^  feet  at  the  lower  end,  to  pass  lightly 
through  the  centre  of  the  arm.  To  keep  the  arm  steady, 
there  is  a  stay-iron  iSi  inches  high,  its  legs  i-2  inch  by 
3'4,  to  stride  2  feet.  The  ring  at  the  top  should  fit  the 
shaft  neatly,  and  be  smooth  and  rounded  inside,  that  it 
may  slide  easily  up  and  down  ;  by  this  the  arm  hangs  to 
the  rope  that  passes  over  a  pulley  at  the  top  of  the  shaft 
8  inches  diameter,  with  a  deep  groove  for  the  rope  or 
cord  to  run  in.  Make  the  leading  arm  6  by  1|  inches 
in  the  middle,  2  by  I  inch  at  the  end,  and  8  feet  long. 
This  arm  must  be  braced  to  the  cog-wheel  above,  to  keep 
it  from  splitting  the  shaft  by  any  extra  stress. 

The  weight  of  the  balance  w  must  be  so  near  equal  to 
the  weight  of  the  arm,  that  when  it  is  raised  to  the  top  it 
will  descend  quietly. 

In  the  bottom  of  the  upright  shaft  is  the  step-gudgeon 
(fig.  15,)  which  passes  through  the  square  plate  4  by  4 
inches,  (fig-.  14,)  on  this  plate  the  arm  rests,  before  the 
flights  touch  the  floor.  The  ring  on  the  lower  end  of  the 
shaft  is  less  than  the  shaft,  that  It  may  pass  through  the 
arm  :  this  gudgeon  comes  out  every  time  the  shaft  is 
taken  out  of  the  arm. 

If  the  machine  is  to  attend  but  one  bolting-hopper,  it 
need  not  be  above  12  or  13  feet  long.  Set  the  upright 
shaft  close  to  the  hopper,  and  the  flights  all  gather  as  the 
end  c  b,  fig.  13.     But  if  it  is  to  attend  for  the  grinding 


240         CONSTRUCTION  OF  MACHINES.  [Chap.  S. 

of  two  pair  of  stones,  and  two  hoppers,  make  it  15  feet 
long,  and  set  it  between  them  a  Httle  to  one  side  of  both, 
so  that  the  two  ends  may  not  both  be  over  the  hoppers 
at  the  same  time,  which  would  make  it  run  unsteady  ; 
then  the  flights  between  the  hoppers  and  the  centre  must 
drive  the  meal  outwards  to  the  sweepers,  as  the  end  c  a, 
%.  13. 

If  it  is  to  attend  two  hoppers,  and  cannot  be  set  be- 
tween them  for  want  of  room,  then  set  the  shaft  near  to 
one  of  them  ;  make  the  flights  that  they  all  gather  to 
the  centre,  and  put  sweepers  over  the  outer  hopper, 
which  will  be  first  supplied,  and  the  surplus  carried  to 
the  other.  The  machine  will  regulate  itself  to  attend 
both,  although  one  should  feed  three  times  as  fast  as  the 
other. 

If  it  be  to  attend  three  hoppers,  set  the  shaft  near  the 
middle  one,  and  put  sweepers  to  fill  the  other  two,  the 
surplus  will  come  to  the  centre  one,  and  it  will  regulate 
to  feed  all  three ;  but  should  the  centre  hopper  ever 
stand  while  the  others  are  going  (of  either  of  these  last 
applications),  the  flights  next  the  centre  must  be  move- 
able that  they  may  be  turned,  and  set  to  drive  the  meal 
out  from  the  centre  ;  hopper-boys  should  be  moved  by 
a  strap  in  some  part  of  their  movement,  that  they  may 
easily  stop  if  any  thing  catch  in  them ;  but  several  in- 
genious mill-wrights  do  prefer  cogs ;  they  should  not 
revolve  more  than  4  times  in  a  minute. 

This  machine  may  be  made  of  a  great  many  diflferent 
forms  and  constructions  on  the  same  principles,  to  an- 
swer the  same  end,  in  a  lesser  degree  of  perfection. 


•   ART.     100. 
OF  THE  DRILL. 


See  the  description,  art.  1.  The  pulleys  should  not 
be  less  than  10  inches  diameter  for  meal,  and  more  for 
wheat.  The  case  they  run  in  is  a  deep  narrow  trough, 
say  16  inches  deep,  4  wide,  pulleys  and  strap  3  inches. 
The  rakes  are  little  square  blocks  of  willow  or  poplar. 


Chap.  3.]     CONSTRUCTION  OF  MACHINES.      241 

or  any  soft  wood,  that  will  not  split  with  the  nails,  all  of 
one  size  that  each  may  take  an  equal  quantity,  nailed  to 
the  strap  with  long,  small  nails,  with  broad  heads,  which 
are  inside  the  strap ;  the  meal  should  be  let  into  them 
always  above  the  centre  of  the  pulley,  or  at  the  top  of  it, 
to  prevent  its  choaking,  which  it  is  apt  to  do,  if  let  in 
low.  The  motion  should  be  slow  for  meal;  but  may 
be  more  lively  for  wheat. 

Directions  for  itsing  a  Hopper-boy. 

1.  When  the  meal-elevator  is  set  in  motion  to  elevate 
the  meal;  the  hopper-boy  must  be  set  in  motion  also,  to 
spread  and  cool  it ;  and  as  soon  as  the  circle  is  full,  the 
bolts  may  be  started ;  the  grinding  and  bolting  may 
likewise  be  carried  on  together  regularly,  which  is  the 
best  way  of  working. 

3.  But  if  you  do  not  choose  to  bolt  as  you  grind,  turn 
up  the  feeding  sweepers  and  let  the  hopper-boy  spread 
and  cool  the  meal,  and  rise  over  it ;  and  when  you  be- 
gin to  bolt  turn  them  down  again. 

3.  If  you  choose  to  keep  the  warm  meal  separate  from 
the  cool,  shovel  about  18  inches  of  the  outside  of  the 
circle  in  towards  the  centre,  and  turn  the  end  flights,  to 
drive  the  meal  outwards  ;  it  will  spread  the  warm  meal 
outwards,  and  gather  the  cool  meal  in  the  bolting-hop- 
per. As  soon  as  the  ring  is  full  with  warm  meal,  rake 
it  out  of  the  reach  of  the  hopper-boy,  and  let  it  fill 
again. 

4.  To  mix  tail-floiver  or  bran,  &c.  with  a  quantity  of 
meal  that  is  under  the  hopper-boy,  make  a  hole  for  it 
in  the  meal  quite  to  the  floor,  and  put  it  in  ;  and  the  hop- 
per-boy will  mix  it  regularly  with  the  whole. 

5.  If  it  does  not  keep  the  hopper  full,  turn  the  feed- 
ing sweeper  a  little  lower,  and  throw  a  little  meal  on  the 
top  of  the  arm,  to  make  it  sink  deeper  into  the  meal.  If 
the  spreading  sweepers  discharge  their  loads  too  soon, 
and  do  not  trail  the  meal  all  around  the  circle,  turn  them 
a  little  lower ;  if  they  do  not  discharge,  but  keep  too  full, 
raise  them  a  little. 

Hh 


342  UTILITY  OF  THE  IMPROVEMENTS.  [Chap.*. 
CHAPTER  IV. 

ART.    101. 

Of  the  utility  of  these  inventions  and  improvements. 

DR.  WISTAR,  of  Philadelphia,  has  discovered  and 
proved  by  many  experiments,  (which  he  communicated 
to  the  American  Philosophical  Society,  and  which  they 
have  published  in  the  3d  volume  of  their  Transactions,) 
that  cold  is  one  principal  agent  in  causing  moisture  to 
evaporate  from  bodies  ;  and  the  fact  is  evident  from  daily 
observation,  viz.  that  it  is  the  different  degrees  of  heat 
and  cold,  between  the  air  and  bodies,  that  causes  them 
to  cast  off  or  contract  moisture. 

1st.  We  see  in  all  sudden  transitions  from  an  extreme 
cold  air  to  a  warm,  that  the  walls  of  houses,  stones, 
ground,  and  every  thing  that  retains  cold,  contracts 
moisture  ;  and  it  certainly  has  the  same  effect  on  meal. 

2.  In  all  sudden  changes  from  warm  to  cold,  every 
thing  casts  off  its  moisture;  for  instance,  what  great 
quantities  of  water  will  disappear  from  the  ground,  in 
one  cold  night ;  this  is  the  reason  why  meal  being  warm 
gets  so  dry  in  cold  weather,  and  bolts  so  free  ;  whereas 
it  is  always  harder  to  bolt  when  there  is  a  change  from 
cold  to  warm. 

3.  If  you  warm  a  razor,  or  a  glass,  warmer  than  your 
breath,  neither  of  them  will  be  sullied  by  it. 

4.  Fill  a  glass  bottle  with  cold  water  in  a  warm  day, 
and  wipe  it  dry,  and  there  will  be  presently  seen  on  its 
outside  large  drops,  collected  from  the  moisture  of  the 
air,  though  the  bottle  still  continues  full. 

From  these  instances,  it  is  evident,  that  the  meal 
should  be  spread  as  thin  as  possible,  and  be  kept  in 
motion  from  the  moment  it  leaves  the  stones,  until  it  is 
cold,  that  it  may  have  a  fair  opportunit}^  of  casting  off 
its  moisture,  which  will  be  done  more  effectually  in  that 
time,  than  can  possibly  be  effected  in  warm  weather,   in 


Chap.  4.]  UTILITY  OF  THE  IMPROVEMENTS.     243 

anv  reasonable  time,  after  it  has  grown  cold  in  a  heap  and 
retained  its  moisture  ;  and  there  is  no  time  for  insects  to 
deposit  their  eggs,  that  may  in  time  breed  the  worms, 
that  are  often  found  in  the  heart  of  barrels  of  flour  well 
packed,  and  by  the  moisture  being  cast  out  more  effec- 
tually, it  will  not  be  so  apt  to  sour.  Therefore  one  great 
advantage  is,  that  the  meal  is  better  prepared  for  boltings 
packin^^  and  keepings  in  much  less  time. 

2.  They  do  the  work  to  much  greater  perfection^  by 
cleaning  the  grain  and  screenings  more  effectually,  hoist- 
ing and  bolting  over  great  part  of  the  flour,  and  grinding 
and  bolting  over  the  middlings,  all  at  one  operation,  mix- 
ing those  parts  that  are  to  be  mixed,  and  separating  such 
as  are  to  be  separated,  more  effectually. 

3.  They  save  much  meal  from  being  wasted^  if  they  be 
well  constructed,  because  there  is  no  necessity  of  tramp- 
ling in  it,  which  trails  it  wherever  we  walk,  nor  shoveling 
it  about  to  raise  a  dust  that  flies  away,  &:c.  This  article 
of  saving  will  soon  pay  the  first  cost  of  building,  and  keep 
them  in  repair  afterwards. 

4.  They  afford  more  room  than  they  take  up,  because 
the  whole  of  the  meal-loft  tliat  heretofore  was  little 
enough  to  cool  the  meal  on,  may  now  be  spared  for  other 
uses,  except  the  circle  described  by  the  hopper-boy:  and 
the  wheat  garners  may  be  filled  from  one  story  to  an- 
other, up  to  the  crane  spout,  above  the  collar-beams  :  so 
that  a  small  part  of  the  house  will  hold  a  quantity  of 
wheat,  and  it  may  be  drawn  from  the  bottom  into  the 
elevator  as  wanted. 

5.  They  tend  to  dispatch  business,  by  finishing  as  they 
go  ;  so  that  there  is  not  as  much  time  expended  in  grind- 
ing over  middlings,  which  w ill  not  employ  the  power  of 
the  mill,  nor  in  cleaning  and  grinding  the  screenings, 
they  being  cleaned  every  few  days,  and  mixed  with  the 
wheat ;  and  as  the  labour  is  easier,  the  miller  can  keep 
the  stones  in  better  order,  and  more  regularly  and  steady 
at  work,  especially  in  the  night  time,  when  they  fre- 
quently stop  for  want  of  help,  whereas  one  man,  would 
be  sufficient  to  attend  six  pair  of  stones  running  (in  one 
house)  well  attended  by  machinery. 


244    UTILITY  OF  THE  IMPROVEMENTS.  [Chap.  4. 

6.  They  last  a  long  time  with  but  little  expense  of  re- 
pair^ because  their  motions  are  slow  and  easy. 

7.  They  hoist  the  grain  and  meal  with  less  power ^  and 
disturb  the  motion  of  the  mill  much  less  than  the  old  way, 
because  the  descending  strap  balances  the  ascending  one, 
so  that  there  is  no  more  power  used,  than  to  hoist  the 
grain  or  meal  itself;  whereas  in  the  old  way  for  every  3 
bushels  of  wheat,  which  fills  a  4  bushel  tub  with  meal, 
the  tub  has  to  be  hoisted,  the  weight  of  which  is  equal 
to  a  bushel  of  wheat,  consequently  the  power  used,  is  as 
3  for  the  elevator  to  4  for  the  tubs,  which  is  one  fourth 
less  with  elevators  than  tubs ;  besides  the  weight  of  4 
bushels  of  \vheat,  thrown  at  once  on  the  wheel,  always 
checks  the  motion,  before  the  tub  is  up ;  the  stone 
sinks  a  little,  and  the  mill  is  put  out  of  tune  every  tubfull, 
which  makes  a  great  difference  in  a  year's  grinding;  this 
is  worthy  of  notice  when  the  water  is  scarce. 

8.  77?^^  save  a  great  expense  of  attenda?ice.  One  half 
of  the  hands  that  were  formerly  required  are  now  suf- 
ficient, and  their  labour  is  easier.  Formerly  one  hand 
was  required  for  every  10  barrels  of  flour  that  the  mill 
made  daily ;  now  one  for  every  20  barrels  is  sufficient. 
A  mill  that  made  40  barrels  a  day,  required  four  men  and 
a  boy ;  two  men  are  now  sufficient. 

Two  mens'  wages,  at  7  dolls,  each,  per  month,  168  dolls. 
Boarding  &c.  for  do.  at  15/.  per  year,     -  80 

One  boy's  board,  clothing,  &c.         -         -         50 

298 

There  appears  a  saving  of  298  dollars  a  year,  in  the 
article  of  wages  and  board,  in  one  double  mill. 

In  support  of  what  is  here  said,  I  add  the  following 
certificates. 

I. 

WE  do  certify,  that  we  have  erected  Oliver  Evanses 
new  invented  mode  of  elevating,  conveying,  and  cool- 
ing meal,  &c.  As  far  as  we  have  experienced,  we  have 
found  them  to  answer  a  valuable  purpose,  well  worthy 
the  attention  of  any  person  concerned  in  merchant,  or 


Chap.4.]  UTILITY  OF  THE  IMPROVEMENTS.    245 

even  extensive  countiy  mills,  who  wishes  to  lessen  the 
labour  and  expense  of  manufacturing  wheat  into  flour. 

JOHN  ELLICOTT, 
JONATHAN  ELLICOTT, 
GEORGE  ELLICOTT, 
NATHANIEL  ELLICOTT. 

Ellicott's  mills, Baltimore  county,  state? 
of  Maryland,  August  4,  1790.  S 

II. 

WE,  the  subscribers,  do  hereby  certify,  that  we  have 
introduced  Oliver  Evans's  improvements  into  our  mills 
at  Brandy  wine,  and  have  found  them  to  answer,  as  re- 
presented to  us  by  a  plate  and  description ;  also  to  be 
a  great  saving  of  waste,  labour  and  expense,  and  not 
subject  to  get  out  of  order.  We  therefore  recommend 
them  as  well  worthy  the  attention  of  those  concerned  in 
manufacturing  grain  into  flour. 

JOSEPH  TATNALL, 
THOMAS  LEA. 
SAMUEL  HOLLINGS WORTH, 
THOMAS  SHALLCROSS^ 
CYRUS  NEWLIN. 
Brandywine  -mills,  3d  ? 
month  28th,  ir91.    5 

III. 

WE  do  certify,  that  we  have  used  Oliver  Evans's 
machinery  for  the  space  of  two  years,  in  our  mills,  at 
Petersburg,  in  Virginia,  consisting  of  three  water-wheels, 
and  three  pair  of  stones ;  and  we  judge  that  they  have 
been,  and  will  continue  to  be,  a  saving  of  300  dollars 
per  year. 


N.  ELLICOTT  &  Co. 


February  20, 1794. 


IV. 


WE  do  certify,  that  we  have  used  Oliver  Evans's 
patent  machinery  in  our  mills  at  Manchester,  in  the 
state  of  Virginia,  consisting  of  three  water-wheels,  and 
three  pair  of  stones,  for  the  space  of  one  year,  and  we 
judge  upon  fair  calculations  that  they  are  a  saving  to  us 
of  300  dollars  per  annum. 

NICHOLSON  &  TAYLOR. 


246  BILLS  OF  MATERIALS.  [Chap.  5. 

Many  more  to  the  same  purpose  might  be  added,  but 
these  may  suffice. 

Supposing  the  reader  is  now  fully  convinced  of  the 
utility  of  these  improvements,  I  proceed  to  give  the  fol- 
lowing bills  of  materials. 


CHAPTER  V. 

BILLS  OF  MATERIALS  TO  BE  PROVIDED    FOR    BUILDING  AND 
CONSTRUCTING  THE  MACHINERY. 

ART.     103. 

For  a  Wheat- Elevator  4<2>  feet  high^  with  a  Strap  4  inches 

wide. 

Three  sides  of  good,  firm,  white  harness-leather. 

220  feet  of  inch  pine,  or  other  boards  that  are  dry,  of 
about  12|  inches  wide,  for  the  cases;  these  are  to  be 
dressed  as  follows: 

86  feet  in  length,  7  inches  wide,  for  the  top  and  bottom. 

86  feet  in  length,  5  inches  wide,  with  the  edges  truly 
squared,  for  the  side  boards. 

A  quantity  of  inch  boards  for  the  garners,  as  they  may 
be  wanted. 

Sheet-iron  or  a  good  butt  of  willow  wood,  for  the  buck- 
ets. 

2000  tacks,  14  and  16  ounce  size,  the  largest  about  half 
an  inch  long,  for  the  buckets. 

31b  of  8d.  and  lib.  of  lOd.  nails,  for  the  cases. 

2  dozen  of  large  wood  screws  (but  nails  will  do)  for  pul- 
ley-cases. 

16  feet  of  2  inch  plank  for  pulleys. 

16  feet  of  ditto,  for  cog  wheels,  and  dry  pine  scantling 
4 1  by  4 1,  or  5  by  5  inches,  to  give  it  motion. 

Smithes  Bill  of  Iron. 

1  double  gudgeon  3  4  inch,  (such  as  fig,  6,  plate  VI.)  5 
inches  between  the  shoulders,  3|  inches  between  the 
holes,  the  necks,  or  gudgeon-part,  3  inches. 


Chap.  S.-]         BILLS  OF   MATERIALS.  247 

1  small  gudgeon,  of  the  common  size,  3-4  inch  thick. 

1  gudgeon  an  inch  thick,  (fig.  7,)  neck  3^  tang.  10  in- 
ches, t')  be  next  the  upper  pulley. 

2  small  bands,  4|  inches  from  the  outsides. 

1  harness-buckle,  4  inches  from  the  outsides,  with  2 

tongues,  of  the  form  of  fig.  12. 
Add  whatever  more  may  be  wanting  for  the  gears,  that 

are  for  giving  it  motion. 

I^or  a  Meal- Elevator  Ai^  Feet  high.  Strap  3|  Inches  wide, 
and  a  Conveyer  for  two  pair  of  Stones. 

S70  feet  of  dry  pine,  or  other  inch  boards,  most  of  them 
Hi  or  12  inches  wide,  of  any  length,  that  they  may 
suit  to  be  dressed  for  the  case  boards,  as  follows  : 

86  feet  in  length,  6|  inches  wide,  for  tops  and  bottoms 
of  the  cases. 

86  feet  in  length,  4|  inches  wide,  for  the  side  boards^ 
truly  squared  at  the  edges. 

The  back  board  of  the  conveyer  trough  15  inches,  bot- 
tom do.  H  inches,  and  front  13  inches  wide. 

Some  2  inch  plank  for  the  pulleys  and  cog-wheels. 

Scantling  for  conveyers  6  by  6,  or  5 1  by  5 1  inches,  of 
dry  pine  or  yellow  poplar ;  (prefer  light  wood)  pine 
for  shafts,  4|  by  ^l  or  5  by  5  inches. 

Si  sides  of  good,  pliant- harness-leather. 

1500  of  14  ounce  tacks. 

A  good,  clean  butt  of  willow  for  buckets,  unless  the 
pieces  that  are  left,  that  are  too  small  for  the  wheat- 
buckets,  will  make  the  meal  buckets. 

41b.  of  8d.  and  lib.  of  lOd.  nails. 

2  dozen  of  large  wood  screws  (nails  will  do)  for  the  pul- 
ley-cases. 

Smithes  Bill  of  Iron. 

1  double  gudgeon,  (such  as  fig.  4,  Plate  VI,)  1|  inch 
thick,  7|  inches  between  the  necks,  3|  between  the 
key-holes,  the  necks  1 1  inch  long,  and  the  tenons  at 
each  end  of  the  same  length,  exacdy  square,  that  the 
socket  may  fit  every  way  alike. 

2  sockets,  one  for  each  tenon,  such  as  appears  on  one 
end  of  fig.  4.     The  distance  between  tlie  outside  of 


248  BILLS  OF  MATERIALS.         [Ghap.  5. 

the  straps  with  the  nails  in,  must  be  5|  inches  ;  fig. 
5  is  an  end  view  of  it,  and  the  band  that  drives  over 
it  at  the  end  of  the  shaft,  as  they  appear  on  the  end  of 
the  conveyer. 

2  small  3-4  inch  gudgeons  for  the  other  ends  of  the  con- 
veyers. 

4  thin  bands  5|  inches  from  the  outsides,  for  the  con- 
veyers. 

1  gudgeon  an  inch  thick,  neck  3^  inches,  and  tang.  10 
inches,  for  the  shaft  in  the  upper  pulley  and  next  to  it ; 
but  if  a  gudgeon  be  put  through  the  pulley,  let  it  be 
of  the  form  of  fig.  6,  with  a  tenon  and  socket  at  one 
end,  like  fig.  4. 

-1  harness-buckle,  3|  inches  from  the  outsides,  with  two 
tongues  ;  such  as  fig.  12,  pi.  6. 
Add  whatever  more  small  gudgeons  and  bands  may 

be  necessary  for  giving  motion. 

For  a  Hopper-Boy^ 

1  piece  of  dry,  hard,  clean,  pine  scantling,  4<|  by  4| 
inches,  and  10  feet  long,  for  the  upright  shaft. 

1  piece  of  dry  poplar,  soft  pine,  or  other  soft  light  wood, 
not  Subject  to  crack  and  split  in  working,  8  by  2| 
inches,  15  or  16  feet  long,  for  the  flight  arms. 

Some  2  inch  plank  for  wheels  to  give  it  motion,  and 
scantling  4^  by  4|  inches  for  the  shafts. 

60  flights  6  inches  long,  3  inches  wide,  and  12  inch  at 
one,  and  1-4  at  the  other  edge,  thinner  at  the  fore  than 
hind  end,  that  they  may  drive  in  tight  like  a  dovetail 
wedge.  These  may  be  made  out  of  green  hard  maple, 
split  from  sap  to  heart,  and  set  to  dry. 

Half  a  common  bed-cord,  for  a  leading  line,  and  balance 
rope. 

Smithes  BjM  of  Iron. 

1  stay-iron,  C  F  E,  plate  VII,  fig.  12.  The  height  from 
the  top  of  the  ring  F,  to  the  bottom  of  the  feet  C  E,  is 
15  inches  ;  distance  of  the  points  of  the  feet  C  E  24 
inches  ;  size  of  the  legs  1-2  by  3-4  inch  ;  size  of  the 
ring  F  J  by  1-4  inches,  round  and  smooth  inside  ;  4 
inches  diameter,  tlie  inside  corners  rounded  off",  to 


Chap.  5-.]      MILL  FOR  HULLING  RICE,  &c.  249 

keep  it  from  cutting  the  shaft;  there  must  be  two  little 

loops  or  eyes,  one  in  each  quarter,  for  the  balance  rope 

to  be  hung  to  either  that  may  suit  best. 
2  screws  (with  thumb-burrs  that  are  turned  by  the  thumb 

and  fingers)  1-4  of  an  inch  thick,  and  3  inches  long^ 

for  the  feet  of  the  stay-iron. 
2  do.  for  the  end  flights,  3|   inches  long,  rounded  1| 

inch  next  the  head,  and  square  1^  inch  next  the  screw, 

the  round  part  thickest. 
2  do.  for  the  end  sweepers,  6|  inches  long,  rounded  1 

inch  next  the  head,  1-4  inch  thick. 
2  do.  for  the  hopper  sweepers,  8|  inches  long  and  1-4 

inch  thick,  (long  nails  with  rivet  heads  will  do.) 
1  step-gudgeon  (fig.  15),  2^  inches  long  below  the  ring, 

and  tang  9  inches,  3-4  inch  thick. 
1  plate  4  by  4,  and  1-8  inch  thick,  for  the  step-gudgeoil 

to  pass  through,  (fig.  14.) 
1  band  for  the  step-gudgeon,  3|  inches  diameter;  frona 

the  outsides  it  has  to  pass  through  the  stay-iron. 
1  gudgeon  and  band,  for  the  top  of  the  shaft,  gudgeon 

3-4  inch,  band  4  inches  diameter  from  the  outsides. 

The  smith  can,  by  the  book,  easily  understand  how 
to  make  these  irons;  and  the  reader  may,  from  these 
bills  of  materials,  make  a  rough  estimate  of  the  whole 
expense,  which  he  will  find  very  low  compared  with 
their  utility. 


ART.    103. 
A  MILL  FOR  CLEANING  AND  HULLING  RICE. 

Plate  X,  fig.  2.  The  rice  brought  to  the  mill  in  boats, 
is  to  be  emptied  into  the  hopper  1,  out  of  which  it  is 
conveyed,  by  the  conveyer,  into  the  elevator  at  S,  which 
elevates  it  into  the  garner  3 ;  on  the  third  floor  it  de- 
scends into  the  gamer  4,  that  hangs  over  the  stones  5, 
and  supplies  them  regularly.  The  stones  are  to  be 
dressed  with  a  few  deep  furrows,  with  but  little  draught, 
and  picked  full  of  large  holes ;  they  must  be  set  more 
than  the  length  of  the  grain  apart.     The  hoop  should  be 

I  i 


250        MILL  FOR  HULLING  RICE,  &c.     [Chap.  5 

lined  inside  with  atrong  sheet-iron  and  if  punched  full 
of  holes  it  will  do  better.  The  grain  is  kept  under  the 
stone  as  long  as  necessary,  by  causing  it  to  rise  some 
distance  up  the  hoop,  to  get  out  through  a  hole,  which 
is  to  be  made  higher  or  lower  by  a  gatej  sliding  in  the 
bottom  of  it. 

The  principle  by  which  the  grain  is  hulled,  is  that  of 
rubbing  them  against  one  another  with  great  force,  be- 
tween the  stones,  by  which  means  they  hull  one  another 
without  being  broke  by  the  stones,  near  as  much  as  by 
the  usual  way.*  As  it  passes  through  the  stones  b,  it 
should  fall  into  a  rolling-screen  or  shaking-sieve  6,  made 
of  wire,  with  such  meshes  as  will  let  out,  at  the  head,  all 
the  sand  and  dust,  which  may  be  let  run  through  the 
floor  into  the  water,  if  convenient ;  and  to  let  the  rice 
and  most  of  the  heavy  chaff  fall  through  into  the  con- 
veyer, which  will  convey  it  into  the  elevator  at  2.  The 
light  chaff,  &c.  that  does  not  pass  through  the  sieve,  will 
fall  out  at  the  tail,  and  if  useless  may  also  run  into  the 
water  and  float  away.  There  may  be  a  fan  put  on  the 
spindle,  above  the  trundle,  to  make  a  light  blast,  to  blow 
out  the  light  chaff  and  dust,  which  should  be  conveyed 
out  through  the  \A'all ;  and  this  fan  may  supercede  the 
necessity  of  the  shaking-sieve.  The  grain  and  heavy 
chaff  are  elevated  into  garner  7,  thence  it  descends  into 
garner  8,  and  passes  through  the  stones  9,  which  are  to 
be  fixed  and  dressed  the  same  way  as  the  others,  and 
are  only  to  rub  the  grain  harder ;  the  sharpness  on  the 
outside  of  the  chaff  (which  nature  seems  to  have  pro- 
vided for  the  purpose),  will  cut  off  all  the  inside  hull 
from  the  grain,  and  leave  it  perfectly  clean ;  then,  as  it 
falls  from  these  stones  it  passes  through  the  wind  of  the 
fan  10,  fixed  on  the  spindle  of  the  stones  9,  which  will 
blow  out  the  chaff  and  dust,  and  drop  them  in  the  room 
21 ;  the  wind  should  escape  through  the  wall.     There 

*  By  trying  many  experiments,  and  with  much  labour,  striving  to  invent 
a  new  machine  fornibbine:  the  dust  off  the  grains  of  wheat,  and  breaking 
thf  lumps  of  dust  mixed  with  wheat  that  is  trod  on  the  ground;  and  for 
shelling  off'  the  white  caps,  breaking  the  rotten,  fly-eaten,  and  smut  grams, 
and  to  bleak  the  jiarlic,  he  I  discovered  this  principle;  which  I  afterwards 
used  Willi  a  common  pair  of  burr  mill-stones,  properly  dressed  for  grind- 
ing wheat,  and  always  found  ii  to  succeed  well,  without  breaking  any  good 
grains,  grinding  the  white  caps  to  fine  dust. 


Chap.  5.]      MILL  FOR  HULLING  RICE,  &c.  251 

is  a  regulating  board  that  moves  on  a  joint  at  21,  so  as 
to  take  all  the  grain  into  the  conveyer,  which  will  con- 
vey into  the  elevator  at  11,  which  elevates  it  into  the 
gamer  IS,  to  pass  through  the  rolling-screen  13,  which 
should  have  wire  of  3  sized  meshes ;  first,  to  take  out 
the  dust,  to  fall  into  a  part  17,  by  itself;  second,  the 
small  rice  into  an  apartment  16  ;  the  whole  grains  fall 
into  gamer  14?,  perfectly  clean,  and  are  drawn  into  bar- 
rels at  15.  The  fan  18  blows  out  the  dust,  and  lodges 
it  in  the  room  1 9,  and  the  wind  passes  out  at  20  5  the 
head  rice  falls  at  the  tail  of  the  screen,  and  runs  into  the 
hopper  of  the  stones  5,  to  go  through  the  whole  opera- 
tion again.  Thus  the  whole  is  completely  done  by  the 
water,  by  the  help  of  the  machinery  from  the  boat,  until 
ready  to  put  into  the  barrel,  without  the  least  manual 
labour. 

Perhaps  it  may  be  necessary  to  make  a  few  fuiTows 
in  the  edge  of  the  stone,  slanting,  at  an  angle  of  about 
30  degrees  with  a  perpendicular  line,  these  furrows  will 
throw  up  the  grain  next  the  stone,  on  the  top  of  that  in 
the  hoop,  which  will  change  its  position  continually,  by 
which  means  it  will  be  better  cleaned ;  but  this  may 
probably  be  done  without. 

Ij 


PART  IV. 

THE 

YOUNG  MILLER'S  GUIDE; 

CONTAINING 

THE  WHOLE  PROCESS 

OF  THE 

ART  OF  MANUFACTURING  GRAIN  INTO  FLOUR; 

EXPLAIJ^ED,  IJV  ALL  ITS  BRAjYCHES, 

ACCORDING  TO  THE  MOST   IMPROVED   PLANS    PRACTISED  IN 

THE  BEST  MERCHANT  AND  FLOUR  MILLS 

IN  AMERICA. 


CONTENTS  OF  PART  IV. 


Cmaf.  I. — The  principles  of  grinding,  and  rules  for 
draughting  the  furrows  of  mill- stones. 

Chap.  II. — Directions  for  furrowing  and  hanging  a  new 
pair  of  burr-stones  ready  for  grinding,  and  keeping 
them  in  good  face,  for  sharpening  them  and  grinding 
to  the  right  fineness ;  so  as  to  clean  the  bran  well, 
and  make  but  little  coarse  flour. 

Chap.  III. — Of  Garlic, — with  directions  for  grinding 
wheat  mixed  with  it,  and  dressing  the  stones  suitable 
thereto. 

Chap.  IV. — Of  grinding  the  middlings,  and  other  coarse 
flour  over  again,  to  make  the  best  profit  of  them. 

Chap.  V. — Of  the  quality  of  stones  to  suit  the  quality 
of  the  wheat. 

Chap.  VI. — Of  bolting-reels  and  cloths,  with  directions 
for  bolting  and  inspecting  flour. 

Chap.  VII. — Of  the  duty  of  the  miller,  in  keeping  the 
business  in  order. 

Peculiar  accidents  by  which  mills  are  subject  to  take 
fire. 

Of  improving  mill-seats. 


Ti!t 


YOUNG  MILLER'S  GUIDE, 


PART  THE  FOURTH 


CHAPTER  I. 

ART.    104. 

THE  PRIN"CIPLES  OP  GRINDING  EXPLAINED,  WITH  SOME  OB- 
SERVATIONS ON  LAYING  OUT  THE  FURROWS  IN  THE  STONES, 
WITH  A  PROPER  DRAUGHT. 

THE  end  we  have  in  view,  in  grinding  the  grain,  is, 
to  reduce  it  to  such  a  degree  of  fineness,  as  is  found  by 
experience  to  make  the  best  bread,  and  to  put  it  in 
SMch  a  state,  that  the  flour  may  be  most  eflfectually  sepa- 
rated from  the  bran  or  skin  of  the  grain,  by  means  of 
sifting  or  bohing ;  and  it  has  been  proved  by  experience, 
that  to  grind  the  grain  fine  with  dull  mill- stones,  will  not 
answer  said  purpose  well,  because  it  kills  or  destroys  that 
lively  quality  of  the  grain,  that  causes  it  to  ferment  and 
raise  in  the  baking ;  it  also  makes  the  meal  so  clammy, 
that  it  sticks  to  the  cloth,  and  chokes  up  the  meshes  in 
bolting.  Hence,  it  appears,  that  it  should  be  made  fine 
with  as  little  pressure  as  possible ;  and  it  is  evident,  that 
this  cannot  be  done  without  sharp  instruments.  Let  us 
suppose  we  undertake  to  operate  on  one  single  grain,  I 
think  it  seems  reasonable  that  we  should  first  cut  it  into 
several  pieces,  with  a  sharp  instrument,  to  put  it  in  a 
state  suitable  for  being  passed  between  two  planes,  in 
order  to  be  reduced  to  one  regular  fineness.     The  planes 

K  k 


258  PRINCIPLES  OF  GRINDING.        [Chap,  i 

should  have  on  their  faces  a  number  of  little  sharp  edges, 
to  scrape  off  the  meal  from  the  bran,  and  be  set  at  such 
a  distance  as  to  reduce  the  meal  to  the  required  fineness, 
and  no  finer,  so  that  no  part  can  escape  unground.  The 
same  rules  or  principles  will  serve  for  a  quantity  that  will 
serve  for  one  grain. 

Therefore,  to  prepare  the  stones  for  grinding  to  the 
greatest  perfection,  we  may  conclude  that  their  faces 
must  be  put  in  such  order,  that  they  will  first  cut  the 
grain  into  several  pieces,  and  then  pass  it  between  them, 
in  such  a  manner,  that  none  can  escape  without  being 
ground  to  a  certain  degree  of  fineness,  and  at  the  same 
time  scrape  the  meal  off  clean  from  the  bran  or  skin. 

1.  The  best  way  that  I  have  yet  found  to  effect  this 
is,  (after  the  stones  are  faced  with  the  staff"  and  the  pick,) 
to  grind  a  few  quarts  of  sharp  fine  sand;  this  will  face 
them  to  fit  each  other  so  exactly,  that  no  meal  can  pass 
between  them  without  being  ground ;  it  is  also  the  best 
way  of  sharpening  all  the  litde  edges  on  the  face,  that 
are  formed  by  the  pores  of  the  stone,  (but  instead  of 
sand,  w^ater  may  be  used,  the  stones  then  face  each 
other)  so  that  they  will  scrape  the  meal  off"  of  the  bran, 
without  too  much  pressure  being  applied.  But  as  the 
meal  will  not  pass  from  the  centre  to  the  periphery  or 
verge  of  the  stones,  soon  enough,  without  some  assist- 
ance, there  must  be  a  number  of  furrows,  to  assist  it  in 
its  egress ;  and  these  furrows  must  be  set  with  such  a 
draught,  that  the  meal  will  not  pass  too  far  along  them 
at  once,  without  passing  over  the  land  or  plane,  lest  it 
should  get  out  unground.  They  should  also  be  of  suf- 
ficient depths,  to  admit  air  enough  to  pass  through  the 
stones  to  carry  out  the  heat  generated  by  the  friction  of 
grinding;  but  if  they  have  too  much  draught,  they  will 
not  bear  to  be  deep,  for  the  meal  will  escape  along  them 
unground.  These  furrows  ought  to  be  made  sharp  at 
the  feather  edge  (which  is  the  hinder  edge  of  the  fur- 
row, and  the  foremost  edge  of  the  land),  which  serves 
the  purpose  of  cutting  down  tlie  grain;  they  should  be 
more  numerous  near  the  centre,  because  there  the  office 
of  the  stone  is  to  cut  the  grain,  and  near  the  periphery 
tlieir  office  is  (that  of  the  two  planes)  to  reduce  the  flour 


Chap.  1.]      PRINCIPLES  OF  GRINDING.  259 

to  its  required  fineness,  and  scFape  the  bran  clean  by  the 
edp^es,  formed  by  the  numerous  little  pores  with  which 
the  burr  stone  abounds.  However,  we  must  consider, 
that  it  is  not  best  to  have  the  stones  too  sharp  near  the 
eye,  because  they  then  cut  the  bran  too  fine.  The  stones 
incline  to  keep  open  near  the  eye,  unless  they  are  too 
close.  If  they  are  porous  (near  the  eye)  and  will  keep 
open  without  picking,  they  will  always  be  a  little  dull, 
which  will  flatten  the  bran,  without  cutting  it  too  much. 
Again,  if  they  be  soft  next  the  eye,  they  will  keep  too 
open,  and  that  part  of  the  stone  will  be  nearly  useless. 
Therefore  they  should  be  very  hard  aud  porous. 

It  is  also  necessary,  that  we  dress  the  face  of  the  stone 
in  such  a  form,  as  to  allow  room-  for  the  grain  or  meal, 
ill  every  stage  of  its  passage  between  the  stones.  In 
order  to  understand  this,  let  us  conceive  the  stream  of 
wheat,  entering  the  eye  of  the  stone,  to  be  about  the 
thickness  of  a  man's  finger,  but  instantly  spreading  every 
■way  over  the  whole  face  of  the  stone ;  therefore  this 
stream  must  get  thinner,  as  it  approaches  the  periphery 
(where  it  would  be  thinner  than  a  fine  hair,  if  it  did  not 
pass  slower  as  it  becomes  finer,  and  if  the  stones  were 
not  kept  apart  by  the  bran),  for  this  reason,  the  stones 
must  be  dressed  so,  that  they  will  not  touch  at  the  cen- 
tre, within  about  a  16th  or  20th  part  of  an  inch,  but  to 
get  closer  gradually,  till  within  about  10  or  \2  inches 
from  the  verge  of  the  stone,  proportioned  to  the  diameter, 
and  from  that  part  out  they  must  fit  nicely  together. 
This  close  part  is  called  the  flouring  of  the  stone.  The 
furrows  should  be  deep  near  the  centre,  to  admit  wheat 
in  its  chopped  state,  and  the  air,  which  tends  to  keep  the 
stones  cool.* 

•  It  is  asserted  by  some  (and  I  believe,  not  without  reason)  that  it  is  ab- 
solutely  necessary  to  have  a  bridge-tree  that  shall  have  a  degree  of  el.sti- 
city,  which  gives  the  stone  a  tremulous  motion  up  and  down,  and  therefore 
effects  a  trituration  more  completely,  making  more  lively  flour  ih;'n  it  would 
do,  supposmg  the  bridge-tree  to  he  a  solid  immoveable  rock-  But  what  is 
the  proper  degree  of  elasticity,  or  size  of  a  bridge  tree,  suitable  to  the 
weight  of  the  stooe,  I  know  not;  not  having  experif-nced  this  matter  suffi- 
ciently to  give  an  opinion  on  it;  but  I  am  inclined  to  think  that  this  is  ai> 
error. 

One  disadvantage  in  having  a  very  elastic  bridge-tree  is,  when  the  stones 
run  empty,  tiiey  come  together  with  more  force,  and  heat  quicker;  and  if 
once  made  red  hot,  it  totally  destroys  the  good  sharp  quality  of  the  burr, 
as  far  as  the  heat  penetrates. 


260  DRAUGHT  OF  MILL-STONES.     [Chap.  1., 

ART.    105. 

OP  THE  DRAUGHT   NECESSARY  TO    BE  GIVEN  TO  THE    FUR- 
ROWS  OF  MILL-STONES 

From  these  principles  and  ideas,  and  the  laws  of  cen- 
tral forces,  explained  art.  13,  I  form  my  judgment  of  the 
proper  draught  of  the  furrows,  and  the  manner  of  dress, 
in  which  I  find  but  few  of  the  best  millers  to  agree ; 
some  prefer  one  kind,  and  some  another,  which  shows 
that  this  necessary  part  of  the  miller's  art  is  not  yet 
generally  well  understood.  In  order  that  this  matter 
may  be  more  fully  discussed  and  better  understood,  I 
have  constructed  fig.  3,  plate  XL  AB  represents  the 
eight  quarter,  CD  the  twelve  quarter,  and  EA  the  cen- 
tral dress.  Now  we  observe  that  in  the  eight  quarter 
dress,  the  short  furrows  at  F  have  about  five  times  as 
much  draught  as  the  long  ones,  and  cross  one  another 
like  a  pair  of  shears,  opened  so  wide  that  they  will  drive 
all  before  them,  and  cut  nothing  ;  and  if  these  furrows 
be  deep  they  will  drive  out  the  meal  as  soon  as  it  gets 
into  them,  and  thereby  make  much  coarse  meal,  such 
as  middlings  and  ship  stuff  or  carnel ;  the  twelve  quarter 
dress  appears  to  be  better ;  but  the  short  furrows  at  G 
have  about  four  times  as  much  draught  as  the  long 
ones,  the  advantage  of  which  I  cannot  yet  see,  because 
if  we  have  once  found  the  draught  that  is  right  for  one 
furrow,  so  as  to  cause  the  meal  to  pass  through  the 
stone  in  a  proper  time,  it  appears  reasonable  that  the 
draught  of  every  other  furrow  should  be  equal  to  it. 

In  the  central  dress  EA  the  furrows  have  all  one 
draught,  and  if  we  could  once  determine  how  much  is 
necessary  exacdy,  then  we  might  expect  to  be  right,  and 
I  presume  we  will  find  it  to  be  in  a  certain  proportion  to 
the  size  and  velocity  of  the  stone  ;  because  the  centri- 
fugal force  that  the  circular  motion  of  the  stones  gives 
the  meal,  has  a  tendency  to  move  it  outward,  and  this 
force  will  be  in  inverse  proportion  to  the  diameter  of 
the  stones,  their  velocities  being  the  samt^  by  the  4'th 
law  of  circular  motion.  E  e  is  a  furrow  of  the  running 
stone,  and  we  may  see  by  the  figure,  that  the  furrows 
cross  one  another  at  the  centre  in  a  much  greater  angle 


Chap.  1.]      DRAUGHT  OF  MILL-STONES.  261 

than  near  the  periphery,  uhich  I  conceive  to  be  right, 
because  the  centrifugal  force  is  much  less  nearer  the 
centre  than  the  periphery.  But  we  must  also  consider, 
that  the  grain,  whole  or  but  little  broken,  requires  less 
draught  and  central  force  to  send  it  out,  than  it  does 
when  ground  fine;  which  shows,  that  we  must  here 
differ  in  practice  from  the  theories  laid  down  in  art.  13, 
founded  on  the  laws  of  circular  motion  and  central  forces; 
because,  the  grain  as  it  is  ground  into  meal,  is  less  affect- 
ed by  the  central  force  to  drive  it  out,  therefore  the  an- 
gles with  which  the  furrows  cross  each  other  must  be 
greater  than  the  verge  or  skirt  of  the  stone,  and  less  near 
its  centre  than  assigned  by  theory,  and  this  variation  from 
theory  can  be  formed  only  by  conjecture,  and  ascertained, 
by  practice. 

From  the  whole  of  my  speculations  on  this  difficult 
subject,  added  to  my  observations  on  my  own  and 
others'  practice  and  experience,  I  attempt  to  form  the 
following  rule  for  laying  out  a  five  foot  mill-stone.  See 
fig.  1.  PI.  XL 

1.  Describe  a  circle  with  3  inches,  and  another  with  6 
inches  radius,  round  the  centre  of  the  stone. 

2.  Divide  the  3  inches  space  between  these  two  circles, 
into  4  spaces,  by  3  circles  equi-distant,  call  these  five 
circles  draught  circles. 

3.  Divide  the  stone  into  5  parts,  by  describing  4  circles 
equi-distant  between  the  eye  and  the  verge. 

4.  Divide  the  circumference  of  the  stone  into  18  equal 
parts,  called  quarters. 

5.  Then  take  a  straight  edged  rule,  lay  one  end  at  one 
of  the  quarters  at  6,  at  the  verge  of  the  stone,  and  the 
other  end  at  the  outside  draught  circle,  6  inches  from 
the  centre  of  the  stone,  and  draw  a  line  for  the  furrow 
from  the  verge  of  the  stone  to  the  circle  5.  Then 
shift  the  rule  from  draught  circle  6,  to  the  draught 
circle  5,  and  continue  the  furrow  line  towards  the 
centre,  from  circle  5  to  4 :  then  shift  in  the  rule  to 
draught  circle  4,  and  continue  to  3;  shift  to  3  and 
continue  to  2;  shift  to  two,  and  continue  to  one,  and  the 
curve  of  the  furrow  is  formed,  as  1 — 6  in  the  figure. 

6.  To  this  curve  form  a  pattern  to  lay  out  all  the  rest  by. 


262  DRAUGHT  OF  MILL-STONES.      [Chap.  1. 

The  furrows  with  this  curve  will  cross  each  other  with 
the  following  angles,  shown  fig.  I, 
at  circle  1,  which  is  the  eve 

of  the  stone  at  75  degrees  angle. 

—  2       -         -  45         

—  3       -         -  35         

—  4       -         -  31         

—  5       -         -  27        

—  6       -         -  23         

These  angles,  I  think,  will  do  well  in  practice,  will 
grind  smooth,  and  make  but  little  coarse  meal,  &c.  as 
shown  by  the  lines  G  r,  H  r,  G  s,  H  s,  &c.  &c. 

Supposing  the  greatest  draught  circle  to  be  6  inches 
radius,  then  by  theory  the  angles  would  have  been 

at  circle  1         -         -  138  degrees  angle, 

—  2         -         -  69         

—  3         -         -  46         

—  4         -         -  34,5      

—  5         -         -  27,5      

—  6         -         -  23         

If  the  draught  circle  had  been  5  inches  radius,  and 
the  furrows  straight,  the  angles  would  then  have  been  at 

circle      degrees. 
1  about  180 

And  6  inches  from  centre,  as  shown  by  ^       ..^ 

lines  Gl, HI.  5  " 

2—60 
3—38 
4—29 
5—23 
6    —       18 
The  angles  near  the  centre  here,  are  quite  too  great 
to  grind ;  they  will  push  the  grain  before  them ;  there- 
fore, to  remedy  all  these  disadvantages,  take  the  afore- 
said rule,  which  forms  the  furrows,  as  shown  at  6 — 7, 
fig.  1,  which  is  4  of  18  qrs.     H  8  represents  a  furrow  of 
the  runner,  showing  the  angles  where  they  cross  those 
of  the  bed- stone,  in  every  part.     Here  I  have  supposed 
the  exti-emes  of  the  draught  to  be  6  inches  for  the  verge, 
and  3  inches  for  the  eye  of  the  stone,  to  be  right  for  a 
stone  5  feet  diameter,  revolving  100  times  in  a  minute; 


Chap.  1.]     DRAUGHT  OF  MILL-STONES.  263 

but  of  this  we  cannot  be  certain.  Yet  by  experience 
and  practice  the  extremes  may  be  ascertained  in  time 
for  all  sizes  of  stones,  with  different  velocities,  no  kind 
of  dress  that  I  can  conceive,  appearing  to  me  likely  to 
be  brought  to  a  truth  except  this,  and  it  certainly  appears 
both  by  inspecting  the  figure,  and  reason,  that  it  will 
grind  the  smoothest  of  all  the  different  kinds  exhibited 
in  the  plate. 

The  principle  of  grinding  is  partly  that  of  shears  clip- 
ping. The  planes  of  the  face  of  the  stones  serving  as 
guides  to  keep  the  grain,  &c.  in  the  edge  of  the  shears, 
the  furrows  and  pores,  forming  the  edges ;  if  the  shears 
cross  one  another  too  short,  they  cannot  cut ;  this  shows 
that  all  strokes  of  the  pick  should  be  parallel  to  the 
furrows. 

To  give  two  stones  of  different  diameters  the  same 
draught,  we  must  make  their  draught  circles  in  direct 
proportion  to  their  diameters :  then  the  furrows  of  the 
upper  and  lower  stones  of  each  size,  will  cross  each 
other  with  equal  angles  in  all  proportional  distances, 
from  their  centres,  to  their  periphery  :  See  art.  13.  But 
when  we  come  to  consider  that  the  mean  circles  of  all 
stones  are  to  have  nearly  equal  velocities,  and  that  their 
central  forces  will  be  in  inverse  proportion  to  the  diame- 
ters ;  we  must  consider,  that  small  stones  must  have 
much  less  draught  than  large  ones,  in  proportion  to 
their  diameters.  See  the  proportion  for  determining  the 
draught,  art.  13. 

It  is  very  necessary  that  the  true  draught  of  the  fur- 
rows, should  be  determined  to  suit  the  velocity  of  the 
stone:  because  the  centrifugal  force  of  the  meal  will 
vary,  as  the  squares  of  the  velocity  of  the  stone,  by  the 
5th  law  of  circular  motion.  But  the  error  of  the  draught 
may  be  corrected,  in  some  measure,  by  the  depth  of  the 
furrows.  The  less  the  draught,  the  deeper  the  furrow  ; 
and  the  greater  the  draught,  the  shallower  must  the  fur- 
row be  to  prevent  the  meal  from  escaping  unground. 
But  if  the  furrows  be  too  shallow,  there  will  not  a  suf- 
ficient quantity  of  air  pass  through  the  stones  to  keep 
them  cool.  But  in  the  central  dress  the  furrows  meet 
so  near  together  that  they  cut  the  stone  too  much  away 


264  OF  FACING  MILL-STONES.      [Oap.  2. 

at  the  centre,  unless  they  are  made  too  narrow ;  there- 
fore, I  prefer  what  is  called  the  quarter  dress  ;  but  divid- 
ed into  so  many  quarters,  that  there  will  be  little  differ- 
ence between  the  draught  of  the  furrows  ;  suppose  18 
quarters  in  a  5  foot  stone;  then  each  quarter  takes  up 
about  10|  inches  of  the  circumference  of  the  stone ; 
which  suits  to  be  divided  into  about  4  furrows  and  4 
lands,  if  the  stone  be  close ;  but  if  it  be  open,  2  or  3 
furrows  to  each  quarter  will  be  enough.  This  rule  will 
give  4  feet  6  inch  stones,  16  ;  and  5  feet  6  inch  stones, 
2t  ;  and  6  feet  stones,  23  quarters.  But  the  number  of 
quarters  is  not  so  particular,  but  better  more  than  less.  If 
the  quarters  be  few,  the  disadvantage  of  the  short  furrows 
crossing  at  too  great  an  angle,  and  throwing  out  the  meal 
too  coarse,  may  be  remedied,  by  making  the  land  widest 
next  the  verge,  thereby  turning  the  furrows  towards  the 
centre,  when  they  will  have  less  draught,  as  in  the  quar- 
ter  H  I,  fig.  3. 


CHAPTER  II. 

Directions  for  Jacing  a  pair  of  new  burr  stones,  laying  out 
the  furrows,  hanging  them  for  grinding,  and  for  keeping 
them  in  good  face ;  picking  and  sharpening  them;  for 
grinding  to  the  right  fineness,  so  as  to  clean  the  bran 
'well,  and  make  but  little  middlings,  ^c. 


ART.    106. 
OP  FACING  MILLSTONES. 

THE  burr  mill-stones  are  generally  left  in  such  face 
by  the  maker,  that  the  miller  need  not  spend  much  la- 
bour and  time  on  them  with  picks,  before  he  may  hang, 
and  grind  water  or  dry  sand,  with  them,  because  he  can 
make  much  better  speed  by  tliis  method.  After  they 
have  ground  a  quantity,  that  may  be  judged  sufficient, 
they  must  be  taken  up,  and  the  red  staff  tiied  over  their 


Chap.  2.]       OF  FACING  MILL-STONES.  265 

faces,*  and  if  it  touches  in  circles,  the  red  parts  should 
be  well  cracked  with  picks,  then  put  them  to  grind  a 
small  quantity  of  water  or  sand  again  ;  after  this  take 
them  up,  and  try  the  staft'  on  them,  picking  off  the  red 
parts  as  before,  and  repeat  this  operation,  until  the  staff 
will  touch  nearly  alike  all  the  way  across,  and  until  the 
stone  comes  to  a  face  in  every  part,  that  the  quality 
thereof  may  plainly  appear ;  then,  with  a  red  or  black 
line  proceed  to  lay  out  the  furrows,  in  the  manner  deter- 
mined upon,  from  the  observations  already  laid  down  in 
ch.  I.     But  here  we  must  observe  that  the  edges  do  the 
grinding,  and  that  the  quantity  ground  will  be  in  propor- 
tion to  the  number  of  edges  that  are  to  do  it.     After 
having  a  fair  view  of  the  face  and  quality  of  the  stone, 
■we  can  judge  of  the  number  of  furrows  most  suitable, 
observing,  that  where  the  stone  is  most  open  and  porous, 
few  furrows  will  be  wanted ;  but  where  it  is  close  and 
smooth,  the  furrows  ought  to  be  more  numerous,  and 
both  tfiey  and  the  lands  narrow,  (about  1  and  1-8  of  an 
inch  wide)  that  they  may  form  the  more  edges,  to  per- 
form the  grinding.     The  furrows,  at  the  back,  should 
be  made  nearly  the*  depth  of  the  thickness  of  a  grain  of 
wheat,  but  sloped  up  to  a  feather  edge,  not  deeper  than 
the  thickness  of  a  finger-nail  ;t  this  edge  is  to  be  made 
as  sharp  as  possible,  which  cannot  be  done  without  a 
very  sharp,  hard  pick.     When  the  furrows  are  all  made, 
try  the  red  staff  over  them,  and  if  it  touches  near  the 

•  The  red  staff  is  longer  than  the  diameter  of  the  stones,  and  three  in- 
ches thick  on  the  edge,  which  is  made  perfectly  straight,  on  which  is  rub- 
bed red  clay,  mixed  with  water;  which  shows  the  highest  parts  of  the 
faces  of  the  stones,  when  rubbed  over  them,  by  leavinij  the  red  on  those 
high  parts. 

t  For  the  form  of  the  bottom  of  the  furrow,  see  plate  XI.  fig.  3.  The 
curve  line  e  b  shows  the  bottom,  b  the  feather  edge,  and  e  the  back  part. 
If  the  bottom  had  been  made  square  at  the  back  as  at  e,  the  grain  would 
lay  in  the  corner,  and  by  the  centrifugal  force,  would  work  out  along  the 
furrows  without  passing  over  the  lands,  and  part  would  escape  unground. 
The  back  edge  must  be  sloped  for  two  reasons  ;  1st,  that  the  meal  may  be 
pushed  on  to  the  feather  edge  ;  2d,  that  the  furrow  may  grow  narrower,  as 
the  face  of  the  stones  wears  away,  to  give  liberty  to  sharpen  the  feather 
edge,  without  making  the  furrows  too  wide.  Fig.  5.  represents  the  face 
of  wo  stones,  working  together,  the  runner  moving  from  a  to  d.  When 
the  furrows  are  right  over  one  another  as  at  a,  there  is  room  for  a  grain  of 
wheat;  when  they  move  to  the  position  of  b,  it  is  flattened,  and  at  c,  is 
clipped  in  two  by  the  feather  edges,  and  the  lands  or  planes  operate  on  it 
asatd- 

L    I 


266  OF  HANGING  MILL-STONES.      [Chap.  2, 

centre,  the  marks  must  be  quite  taken  off  about  a  foot 
next  to  it,  but  observing  to  crack  lighter  the  farther  from 
it,  so  that  when  the  stones  are  laid  together,  they  will  not 
touch  at  the  centre,  by  about  one  twentieth  part  of  an 
inch,  and  close  gradually,  so  as  to  touch  and  fit  exactly, 
for  about  10  or  12  inches  from  the  verge.  If  the  stones 
be  now  well  hung,  having  the  facing  and  furrowing  neatly 
done,  they  will  be  found  in  the  most  excellent  order  for 
8;rinding  wheat,  that  they  can  possibly  be  put  in,  because 
they  are  in  good  face,  fitting  so  neatly  together,  that  the 
wheat  cannot  escape  unground,  and  all  the  edges  being 
at  their  sharpest,  so  that  the  grain  can  be  ground  into 
flour,  with  the  least  pressure  possible. 


ART.    107. 

OF  HANGING  MILL  STONES. 

• 

If  the  stone  have  a  balance-ryne  it  is  an  easy  matter 
to  hang  it,  for  we  have  only  to  set  the  spindle  perpendi- 
cular to  the  face  of  the  bed-stone ;  ^\hich  is  done  by 
fastening  a  staff  on  the  cock-head  of  the  spindle,  so  that 
the  end  may  reach  to  the  edge  of  the  stone,  and  be  near 
the  face.  In  this  end  we  put  a  piece  of  whale-bone  or 
quill,  so  as  to  touch  the  stone,  that,  when  one  turns  the 
trundle-head,  the  quill  will  move  round  the  edge  of  the 
stone,  and  when  it  is  made  to  touch  alike  all  the  way- 
round,  by  altering  the  wedges  of  the  bridge,  the  stone 
may  be  laid  down  and  it  will  be  ready  hung;*  but  if  we 
have  a  stiff-ryne,  it  will  be  much  more  difficult,  because 
we  have  not  only  to  fix  the  spindle  perpendicular  to  the 

*  But  here  we  must  observe,  whether  tbe  stone  be  of  a  true  balance,  as 
It  hangs  on  the  cock  head,  and  if  not,  it  must  be  truly  balanced,  b}  running 
le;'d  into  the  1  ghiesi  side-  This  ought  to  be  carefully  attended  to  by  the 
maker,  because  the  s'one  may  be  made  to  b;  lance  truly  v.'hen  at  resi  ;  yet, 
if  every  opposite  p  irt  does  not  balance  each  other  truly,  the  stone  may 
be  greatly  out  of  balance  when  in  motion,  aithoMt^h  truly  balanced  when  at 
rest;  and  this  is  the  reason  why  the  hush  of  some  stones  cannot  be  kept 
tight  hut  a  few  hours,  while  others  Will  keep  t  gtr  several  months,  the 
spindles  being  good,  and  stones  balaiu  ed  when  at  rest-  The  reason  why  a 
stone  that  is  balanced  at  rest,  will  sometimes  not  be  balanced  in  motion,  is, 
that  if  the  upper  side  be  heaviest  on  one  side,  sind  the  lowest  side  be  hea- 
viest on  the  other  side  of  the  centre,  the  stone  may  balance  al  res',  yet, 
when  set  in  motion,  the  heaviest  parts  draw  o\it\iards  most  by  the  centrifu- 
sjal  force,  which  v/ill  put  the  stone  out  ol  balance  while  in  motion  ;  and  if 


Chap.  2.]     OF  HANGING  MILL-STONES.  26r 

face  of  the  bed-stone,  but  we  must  set  the  face  of  the 
runner  perpendicular  to  the  spindle,  and  all  this  must  be 
done  to  the  greatest  exactness,  because  the  ryne  being 
stiff,  will  not  give  way  to  suffer  the  runner  to  form  itself 
to  the  bed-stone,  as  will  the  balance-ryne. 

The  bed  of  the  ryne  being  first  carefully  cleaned  out, 
the  ryne  is  put  into  it  and  tied,  until  the  stone  is  laid 
down  on  the  cock-head  ;  then  u  e  find  the  part  that  hangs 
lowest,  and,  by  putting  the  hand  thereon,  we  press  the 
stone  down  a  little,  turning  it  about  at  the  same  time, 
and  observing,  whether  the  lowest  part  touches  the  bed- 
stone equally  all  the  way  round ;  if  it  does  not,  it  is 
adjusted  by  altering  the  wedges  of  the  bridge-tree,  until 
it  touches  equally,  and  then  the  spindle  will  stand  per- 
pendicular to  the  face  of  the  bed-stone.  Then,  to  set 
the  face  of  the  runner  perpendicular  or  square  to  the 
spindle,  we  stand  in  one  place,  turning  the  stone,  and 
pressing  on  it  at  every  horn  of  the  ryne,  as  it  passes,  and 
observing  whether  the  runner  will  touch  the  bed-stone 
equally,  at  every  horn,  which,  if  it  does  not,  we  strike 
with  an  iron  bar  on  the  horn,  that  bears  the  stone  high- 
est, which,  by  its  jarring,  will  setde  itself  better  into  its 
bed,  and  thereby  let  the  stone  down  a  little  in  that  part ; 
but  if  this  be  not  sufficient  there  must  be  paper  put  on 
the  top  of  the  horn,  that  lets  the  stone  too  low  ;  observ- 
ing to  mark  the  high  horns,  that  when  the  stone  is  taken 
up,  a  little  may  be  taken  off  the  bed,  and  the  ryne  will 
soon  become  so  neatly  bedded,  that  the  stone  will  hang 
very  easily.  But  I  have  ever  found  the  bridge  to  be  a 
little  out  of  place,  or  in  other  words  the  spindle  moved 
a  little  from  its  true  perpendicular  position,  with  respect 
to  the  face  of  the  bed-stone,  at  every  time  the  stone  is 

the  stone  be  not  round,  the  parts  farthest  from  the  centre  will  have  ths 
greatest  centrifugal  force,  because  the  centrifugal  force  is  as  the  square  of 
the  distance  from  the  centre.  The  neck  of  the  spindle  wll  wear  nest  the 
lonfrest  side,  and  get  bush  loose  ;  and  this  argues  in  favour  of  a  stiff  ryne. 
The  best  method  that  I  have  heard  of  for  hanging  siones  with  stiff  horned 
rynes,  appears  to  be  as  follows-  Fix  a  screw  to  each  horn  to  regulate  by, 
which  is  done  thus — after  the  horns  are  bedded,  sink  under  each  horn  a 
strong  burr,  through  which  the  screw  is  to  pass  from  the  back  of  the  stone, 
and  fasten  them  in  with  lead  ;  ihen,  after  the  siont-  is  laid  down,  put  in  the 
acrews  from  the  top  of  the  stone,  screwing  them  till  the  points  bear  tight 
on  the  horn  :  then  proceed  to  hang  the  stone,  which  is  very  easily  done, 
by  turninij  the  screws. 


268  OF  REGULATING  THE  FEED,  &c.  [Chap.  2. 

taken  up ;  which  is  a  great  objection  to  the  stifF  horn 
ryne ;  for  if  the  spindle  be  but  very  little  out  of  place,  the 
stones  cannot  come  together  equally;  whereas  if  it  be 
considerably  out  of  place  with  a  balance  ryne,  it  will  be 
little  or  no  injury  to  the  grinding,  because  the  running 
stone  has  liberty  to  form  itself  to  the  bed- stone. 


ART.    108. 
OF  REGULATING  THE  FEED  AND  WATER  IN  GRINDING. 

The  stone  being  well  hung,  proceed  to  grind,  and 
when  all  things  are  ready,  draw  as  much  water  as  is 
judged  to  be  sufficient ;  then  observe  the  motion  of  the 
stone,  by  the  noise  of  the  damsel,  and  feel  the  meal ;  and 
if  it  be  too  coarse,  and  the  motion  too  slow,  give  less  feed, 
and  she  Mill  grind  finer,  and  the  motion  will  be  quicker  ; 
if  it  grind  too  coarse  yet,  lower  the  stone ;  then  if  the 
motion  be  too  slow  draw  a  little  more  water ;  but  if  the 
meal  feel  to  be  too  low  ground,  and  the  motion  right, 
raise  the  stone  a  litde,  and  give  a  litde  more  feed.  If  the 
motion  and  feed  be  too  great,  and  the  meal  be  ground  too 
low,  shut  oif  part  of  the  water. 

But  if  the  motion  be  too  slow,  and  feed  be  to  small, 
draw  more  water. 

To  regulate  the  grinding  to  suit  the  quantity  of  water, 
the  following  rule  is  set  in  verse,  that  it  may  be  more 
easily  remembered.* 

RULE. 

If  the  motion  be  too  great, 
Then  add  a  little  feed  and  weight; 
But  if  the  motion  be  too  slow, 
Less  feed  and  weight  will  let  her  go. 

But  here  the  miller  must  remember,  that  there  is  a 
certain  portion  of  feed  that  the  stones  will  bear  and  grind 

*  The  miller  should,  by  many  experiments,  find  the  quantity  of  water 
that  best  suits  his  mill,  aid  have  a  mark  made  on  the  stafF  by  which  he 
draws  the  gate,  that  he  may  draw  a  suitable  quantity  at  once. 


Chap.2.]  OF  REGULATING  THE  FEED,  &c.  269 

well;  which  will  be  in  proportion  to  the  size,  velocity 
and  sharpness  of  them,  and  if  this  be  exceeded,  there 
%vill  be  a  loss  by  not  having  the  grinding  well  done. 
But  no  rule  can  be  laid  down,  to  ascertain  this  portion  of 
feed ;  it  must  be  attained  by  practice  ;*  as  must  also  the 
art  of  judging  of  the  right  fineness.  I  may,  however,  lay 
down  such  rules  and  directions  as  may  be  of  some  as- 
sistance to  the  young  beginner. 


ART.     109. 
RULE  FOR  JUDGING  OF  GOOD  GRINDING. 

Catch  your  hand  full  of  the  meal  as  it  falls  from  the 
stones,  and  feel  it  lightly  between  your  fingers  and 
thumb ;  and  if  it  feels  smooth  and  not  oily  or  clammy, 
and  wiU  not  stick  much  to  the  hand,  it  shows  it  to  be 
fine  enough,  and  the  stones  to  be  sharp.  If  there  be  no 
lumps  to  be  felt  larger  than  the  rest,  but  all  of  one  fine- 
ness, it  shows  the  stones  to  be  well  faced,  and  the  fur- 
rows to  have  not  too  much  draught,  as  none  has  escaped 
unground. 

But  if  the  meal  feels  very  smooth  and  oily,  and  sticks 
much  to  the  hand,  it  shows  it  to  be  too  low  ground,  hard 
pressed  and  the  stones  dull. 

But  if  it  feels  part  oily,  and  part  coarse  and  lumpy, 
and  will  stick  much  to  the  hand,  it  shows  that  the  stones 
have  too  much  feed ;  or,  that  they  are  dull,  and  badly 
faced,  or  have  some  furrows  that  have  too  much  draught ; 
or  are  too  deep,  or  perhaps  too  steep  at  the  back  edge, 
as  part  has  escaped  unground,  and  part  too  much  pressed 
and  low. 

Catch  your  hand  full,  and  holding  the  palm  up,  shut 
it  briskly ;  if  the  greatest  quantity  of  the  meal  fly  out  and 
escape  between  your  fingers,  it  shows  it  to  be  in  a  fine 
and  lively  state,  the  stones  sharp,  the  bran  thin,  and  will 
bolt  well :  But  the  greater  the  quantity  that  stays  in  the 
hand,  the  more  it  shows  the  reverse. 

*  If  the  stones  be  over-fed,  it  is  not  possible  that  the  bran  should  be 
■well  cleaned,  because  the  sharp  edges  on  ilit-  face  of  ihe  stone,  tliai  is 
made  for  the  purpose  of  scraping  the  bran  clean,  is  kepi  from  it  by  the 
quantity  of  meal  that  is  between  the  stones. 


270  OF  REGULATING  THE  FEED,  &c.  [Chap.  2. 

Catch  a  hand  full  of  meal  in  a  sieve,  and  sift  the  meal 
clean  out  of  the  bran  ;  then  feel  it,  and  if  it  feels  soft  and 
springing,  or  elastic,  and  also  feels  thin,  with  but  little 
sticking  to  the  inside  of  the  bran,  and  no  pieces  found 
much  thicker  than  the  rest,  will  show  the  stones  to  be 
shar[),  and  the  grinding  well  done.* 

But  if  it  is  broad  and  stiff,  and  the  inside  white,  it  is  a 
sure  sign  that  the  stones  are  dull  or  overfed.  If  you  find 
some  parts  that  are  much  thicker  and  harder  than  the  rest, 
such  as  almost  half  or  quarter  grains,  it  shoAvs  that  there 
are  some  furrows  that  have  too  much  draught,  or  are  too 
deep  or  steep,  at  the  back  edge ;  else,  that  you  are  grind- 
ing with  less  feed  than  the  depth  of  the  fun-ows,  and  ve- 
locity of  the  stone  will  bear. 


ART.    110. 
OF  DRESSING  AND  SHARPENING  THE  STONES  WHEN  DULL 

When  the  stones  get  dull  they  must  be  taken  up,  that 
they  may  be  sharpened  ;  to  do  this  in  the  best  manner, 
we  must  be  provided  with  sharp  hard  picks,  with  which 
the  feather  edge  of  the  furrows  are  to  be  dressed  as  sharp 
as  possible ;  which  cannot  be  done  with  soft  or  dull 
picks.  The  bottoms  of  the  furrows  are  likewise  to  be 
dre'-sed,  to  keep  them  of  the  proper  depth ;  but  here  the 
dull  picks  may  be  used.f  The  straight  staff  must  now 
also  be  run  over  the  face  carefully,  and  if  there  be  any 
parts  harder  or  higher  than  the  rest,  the  red  will  be  left 
on  them  ;  which  must  be  cracked  lightly,  with  many 
cracks,  to  make  them  wear  as  fast  as  the  softer  parts,  in 
order  to  keep  the  face  good.    These  cracks  do  also  form 

•  Instead  of  a  sieve,  you  may  take  a  shovel  and  hold  the  point  near  the 
stream  of  meal,  and  it  will  catch  part  of  the  bran,  with  but  little  meal  mix- 
ed  with  it;  whicli  may  be  separated  by  tossing  it  from  one  hand  to  the 
other,  Wiping^  the  hand  at  each  toss. 

f  To  prevent  the  steel  from  striking  your  fingers,  take  a  piece  of  lea- 
ther about  5  by  6  inches  square,  make  a  hole  through  the  middle,  and  put 
the  handle  of  the  pick  through  it,  keeping  it  between  your  hands  and  the 
pick,  uiakiufj  a  loop  in  the  lower  edge,  through  which  put  one  of  your  fiu- 
gers,  to  keep  up  the  lower  part  from  the  stone. 


Oiap.2.]  DEGREE  OF  FINENESS  FOR  FLOUR.    271 

edges  that  help  to  clean  the  bran ;  and  the  harder  and 
closer  the  stone,  the  more  numerous  are  they  to  be.  They 
are  to  be  made  with  a  very  sharp  pick,  parallel  to  the 
furrows ;  and  the  damper  the  grain,  the  more  the  stone 
is  to  be  cracked,  and  the  drier  and  harder,  the  smoother 
must  the  face  be.  The  hard  smooth  places  which  glaze, 
may  be  made  to  wear  more  evenly,  by  striking  them, 
either  with  a  smooth  or  rough  faced  hammer  many  light 
strokes,  until  a  dust  begins  to  appear,  which  frets  the 
flinty  part,  and  makes  it  softer  and  sharper.  The  stone 
will  never  be  in  the  best  order  for  cleaning  the  bran, 
without  first  grinding  a  little  sand,  to  sharpen  all  the  little 
edges  formed  by  the  pores  of  the  stone  ;  the  same  sand 
may  be  used  several  times.  The  stones  may  be  sharpened 
without  being  taken  up,  or  even  stopped,  viz.  take  half 
a  pint  of  sand,  and  hold  the  shoe  from  knocking,  to  let 
them  run  empty  ;  then  pour  in  the  sand,  and  this  will 
take  the  glaze  off  the  face,  and  whet  up  the  edges  so 
that  they  will  grind  considerably  better :  this  ought  to 
be  often  done.* 

Some  are  in  the  practice  of  letting  stones  run  for 
months  without  being  dressed ;  but  I  am  well  convinced 
that  those  who  dress  them  well  twice  a  week,  are  well 
paid  for  their  trouble. 


ART.    111. 

OP  THE  MOST  PROPER  DEGREE  OF  FINENESS  FOR  FLOUR. 

As  to  the  most  proper  degree  of  fineness  for  flour, 
millers  differ  in  their  opinion  ;  but  a  great  majority,  and 
many  of  the  longest  experience,  and  best   judgment, 

•  But  care  should  be  taken  to  prevent  the  sand  from  getting  mixed  with 
the  meal ;  it  sliould  be  caiciied  in  some  vessel,  the  stone  being  suffered  to 
run  quite  empty;  the  sm^ll  quantity  thut  will  remain  in  the  stone  will  not 
injure  the  Bour  But  I  do  not  wish  to  encourage  a  lazy  miller,  to  neglect 
taking  «ip  the  stone. 

When  stones  are  first  set  to  grind,  they  incline  to  raise,  and  grind  coarser 
for  a  considerable  time,  the  true  reason  of  which  is  difficult  to  assign. 
Some  attribute  it  to  the  expansion  of  the  metal  in  the  spindle  ;  it  has  been 
suggested  to  me,  that  it  is  the  steam,  or  the  rarification  of  the  air,  by  the 
heal  produced  by  the  action  of  the  stones,  which,  not  having  a  perfectly  free 
passage  to  escape,  bears  up  a  part  of  the  weight  of  the  stone  ;  and  this 
catise  will  increase,  until  the  stones  are  heated  to  the  greatest  degree. 


272    DEGREE  OF  FINENESS  FOR  FLOUR.  [Chap.  2. 

agree  in  this ;  that,  if  the  flour  be  made  very  fine,  it  will 
be  killed  (as  it  is  termed) ;  so  that  it  will  not  raise,  or 
ferment  so  well  in  baking;  but  I  have  heard  several 
millers  of  good  judgment,  give  it  as  their  opinion,  that 
flour  cannot  be  made  too  fine,  if  ground  with  sharp  clean 
stones;  provided  they  are  not  suffered  to  rub  against 
each  other ;  and  some  of  those  millers  do  actually  re- 
duce almost  all  the  meal  they  get  out  of  the  wheat  into 
superfine  flour ;  by  which  means  they  have  but  two 
kinds,  viz.  superfine  flour,  and  horse  feed,  which  is  what 
is  left  after  the  flour  is  made,  and  is  not  fit  to  make  even 
tlie  coarsest  kind  of  ship-bread. 

I  have  tried  the  following  experiment,  viz.  I  contrived 
to  catch  as  much  of  the  dust  of  flour  that  was  floating 
about  in  the  mill,  as  made  a  large  loaf  of  bread,  which 
was  raised  with  the  same  yeast,  and  baked  in  the  same 
oven,  with  other  loaves,  that  were  made  out  of  the  most 
lively  meal ;  when  the  loaf  made  of  tlie  dust  of  the  flour 
was  equally  light,  and  as  good,  if  not  better  than  any  of 
the  others  ;  it  being  the  moistest,  and  pleasantest  tasted, 
though  made  of  flour  that  felt  like  oil,  it  being  so  very 
fine. 

I  therefore  conclude,  that  it  is  not  the  degree  of  fine- 
ness that  destroys  the  life  of  the  flour,  but  the  degree  of 
pressure  applied  on  it  in  grinding ;  and  that  flour  may 
be  reduced  to  the  greatest  degree  of  fineness,  without 
injuring  the  quality ;  provided,  it  be  done  with  sharp 
clean  stones,  and  little  pressure.* 

•  It  might  be  difficult  to  assij^n  the  true  reason  why  pressure  or  heat 
has  such  an  effect  on  flour,  as  to  destroy  that  life  or  principle,  that  causes 
it  to  ferment  and  raise  in  the  baking — Bui  we  may  form  a  few  conjectures. 

Q'lery,  may  not  this  life  be  that  vegetative  quality  that  causes  the  grain 
to  grow,  seeing  it  is  a  fact  known  by  experience,  that  if  the  grain  be  dam- 
aged, either  by  wet  op  heating  in  a  heap  so  as  to  destroy  its  vegetation,  that 
the  flour  that  is  made  thereof  will  not  bake  well  ?  And  I  presume,  that  if 
grain  be  heated  by  any  means,  so  as  to  destroy  its  vegetative  quality,  it  will 
not  make  flour  that  will  have  an  easy  fermentation ;  and  it  is  probable,  that 
this  degree  of  heat  is  generated  by  the  act  of  grinding  when  great  pressure 
is  applied,  which  cannot  be  avoided  if  the  stones  be  dull. 

But  again,  if  we  consider  that  most  bodies  are  in  part  composed  of  air, 
which  is  in  a  solid  and  fixed  state,  and  constitutes  a  proportional  part  of 
their  weight,  and  this  proportion  is  diflTerent  in  different  species  of  matter, 
from  1-16  to  1-2,  and  in  one  species  of  wheat  has  been  found,  by  experi- 
ments,  to  be  1-5  of  its  whole  weight ;  that  is,  121b.  of  fixt  d  air  in  60ib.  or 
one  bushel  of  wheat.  Now  this  air  is  roused  into  action  two  ways,  viz.  by 
fermentation  and  by  heat,  and  as  fast  as  it  is  roused,  it  instantly  leaves  the 


Chap.  3.]  OF  GARLIC,  &c.  273 

CHAPTER  III. 

ART.    112. 

OF  G\RLTC,  WITH  DIRECTIQNS  FOR  GRINDING  WHEAT  MIXED 
THKRKWITH;  AND  FOR  DRESSING  THE  STONES  SUITABLE 
THERKTO. 

IN  many  parts  of  America  there  is  a  species  of  onion 
called  garlic,  that  grows  spontaneously  with  the  wheat. 
It  bears  a  head  resembling  a  seed  onion,  which  contains 
a  number  of  grains  about  the  size  of  a  grain  of  wheat, 
but  somewhat  lighter.*  It  is  of  a  glutinous  substance, 
which  very  soon  adheres  to  the  stone  (in  grinding)  in 
such  a  manner  as  to  blunt  the  edges,  that  they  will  not 
grind  to  any  degree  of  perfection.  Therefore,  as  often 
as  the  stones  become  dull,  we  are  obliged  to  take  the 

body,  and  expands  itself  into  about  a  million  times  more  space  than  it  fill- 
ed  before,  in  the  form  of  a  dense  body.  See  Martm's  Philosopiiy.  New- 
cider  contains  a  large  portion  of  this  fixed  air,  whch  flies  off  by  fermenta- 
tion, leaving  the  cast  consider,  bly  emptied;  and  as  soon  as  the  fixed  air 
is  all  gone,  the  fermentation  ceases- 

Query,  Is  not  this  fixed  air  the  very  soul  of  vegetation  and  fermentation, 
and  may  not  the  degree  of  heat  generated  by  grinding  witli  great  pressure, 
set  it  in  motion  and  cause  it  to  leave  the  floir,  thereby  not  only  destroying 
its  life,  but  greatly  lessening  its  weight,  to  the  great  loss  of  the  miller; 
who,  although  he  expects  by  hard  squeezmg  to  gain  profit,  sustains  loss  ? 
As  a  confirmation  of  this  hypotliesis,  we  may  observe,  that  many  experi- 
ments have  been  made,  by  weighing  a  quantity  of  wheat  carefully,  before 
it  was  ground,  and  then  weighing  every  thing  that  it  made  in  manufactur- 
ing, and  we  have  found  it  to  be  lacking  in  weight  from  1  to  5  lb.  per  b  .sh- 
el :  which  could  not  be  accounted  tor  any  way  better,  than  supposing  the 
loss  to  be  occasioned  by  the  escape  of  the  fixed  air.  Therefore,  I  con- 
cltide,  that  the  stones  ought  to  rtvohe  slow  and  be  kept  sharp;  and  the 
larijer  they  are,  the  slower  will  they  require  to  go,  and  the  lighter  may  tfiey 
press  ihe  grain,  and  yet  grind  a  sufficient  quantity,  and  make  the  bes'  fiour. 

*  The  complete  separation  ot  this  garlic  from  the  wheat,  is  so  difficult, 
that  it  has  hitherto  baffl.,-d  all  our  art.  Those  grains  that  are  larger,  and 
those  that  are  smaller,  can  be  separated  by  screens ;  and  those  that  are 
much  lighter,  may  be  blown  out  by  fans  ;  but  those  that  are  of  the  same 
size,  and  nearly  of  the  same  weight,  cannot  be  separated  without  putting 
the  wheat  in  water,  where  the  wheat  will  sink,  and  the  garbc  swim.  But 
this  method  is  too  tedious  tor  the  miller  to  practise,  except  it  be  once  a 
year,  to  clean  up  the  headings,  or  the  like,  rc'ther  than  lose  the  wheat  that 
is  mixed  with  the  garlic,  which  cannot  be  otherwise  sufHcifntly  separated. 
Great  care  should  be  tak'^n  by  the  farmers  to  prevent  this  troublesome 
thing  from  getting  root  in  their  farms,  which,  if  it  does,  it  will  be  almost 
impossible  ever  to  root  it  out  again;  because  it  propagates  by  both  seed 
and  root,  and  is  very  hardy. 

M  m  • 


274  OF  GARLIC,  &c.  [Chap.  3. 

runner  up,  and  wash  the  glaze  off  with  water,  scrubbing 
the  faces  with  stiff  brushes,  and  drying  up  the  water 
with  cloths  or  sponges  ;  this  laborious  operation  must 
be  repeated  twice,  or  perhaps  four  times,  in  24  hours ; 
if  there  be  about  10  grains  of  garlic  in  a  handful  of 
wheat. 

To  put  the  stones  in  the  best  order  to  grind  garlicky 
wheat,  they  must  be  cracked  roughly  all  over  the  face  ; 
and  dressed  more  open  about  the  eye,  that  they  may  not 
break  the  grains  of  garlic  too  suddenly,  but  gradually 
giving  the  glutinous  substance  of  the  garlic  more  time  to 
incorporate  itself  with  the  meal,  that  it  may  not  adhere 
to  the  stone.  The  rougher  the  face,  the  longer  will  the 
stones  grind,  because  the  longer  will  the  garlic  be  in  fill- 
ing all  the  edges. 

The  best  method  that  I  have  yet  discovered  for  manu- 
facturing garlicky  wheat,  is  as  follows,  viz. 

First,  clean  it  over  several  times,  in  order  to  take  out 
all  the  garlic  that  can  be  got  out  by  the  machinery, 
(which  is  easily  done  if  you  have  a  wheat  elevator  well 
fixed,  as  directed  in  art.  94,  plate  IX.)  then  chop  or  half 
grind  it,  which  will  break  the  garlic,  (it  being  softer  than 
the  wheat)  the  moisture  of  which,  will  so  diffuse  itself 
through  the  chopped  wheat,  that  it  will  not  injure  the 
stones  so  much,  in  the  second  o:rindin2:.  Bv  this  means 
a  considerable  quantity  can  be  ground,  without  taking 
up  the  stones.  The  chopping  may  be  done  at  the  rate 
of  15  or  20  bushels  in  an  hour ;  and  with  but  little  trou- 
ble or  loss  of  time ;  provided  there  be  a  meal-elevator 
that  will  hoist  it  up  to  the  meal-loft,  from  whence  it  may 
descend  to  the  hopper  by  spouts,  to  be  ground  a  second 
time;  when  it  will  grind  faster  than  if  it  had  not  been 
chopped.  Great  care  should  be  taken,  that  it  be  not 
chopped  so  fine  that  it  will  not  feed  by  the  knocking  of 
the  shoe ;  (which  would  make  it  very  troublesome)  as 
likewise,  that  it  be  not  too  coarse,  lest  the  garlic  be  not 
sufficiently  broken.  If  the  chopped  grain  could  lay  a 
considerable  time,  that  the  garlic  may  dry,  it  would 
grind  much  better. 

But  although  every  precaution  be  taken,  if  there  be 
much    garlic    in  the  wheat,  the  bran  will  not  be  well 


Chap.  4]  OF  GRINDING  MIDDLINGS,  &c.  275 

cleaned  ;  besides,  there  will  be  much  coarse  meal  made  ; 
such  as  middlings,  and  stuff;  which  will  require  to  be 
ground  over  again,  in  order  to  make  the  most  profit  of 
the  grain  :  this  I  shall  tieat  of  in  the  next  chapter.* 


CHAPTER  IV. 

ART.    113. 

OF  GRINDING  OVER   THE   MIDDLINGS,  STUFF  AND   BRAN,  OR 
SHORTS,  IF  NECESSARY;   TO  MAKE  THE   MOST  OF  THEM. 

ALTHOUGH  we  grind  the  grain  in  the  best  man- 
ner we  possibly  can,  so  as  to  make  any  reasonable  de- 
spatch ;  yet  there  will  appear  in  the  bolting,  a  species  of 
coarse  meal,  called  middlings;  and  stuff,  a  quality  be- 
tween superfine  and  shorts;  which  will  contain  a  por- 
tion of  the  best  part  of  the  grain  :  but  in  this  coarse  state 
they  will  make  very  coarse  bread  ;  consequently,  will 
command  but  a  low  price.  For  which  reason  it  is  often- 
times more  profitable  to  tlie  miller  to  grind  and  bolt  such 
over  again,  and  make  them  into  superfine  flour,  and 
fine  middlings ;  this  may  easily  be  done  by  proper  ma- 
nagement. 

The  middlings  are  generally  hoisted  by  tubs,  and  laid 
in  a  convenient  place  on  the  floor,  in  the  meal-loft,  near 
the  hopper-boy,  until  there  is  a  large  quantity  gathered  : 
when  the  first  good  opportunity  offers  it  is  bolted  over, 
without  any  bran  or  .shorts  mixed  with  it,  in  order  to 
tkke  out  all  that  is  already  fine  enough  ;  which  will  pass 
through  the  superfine  cloth.  The  middlings  will  pass 
through  the  middlings'  cloth,  and  will  then  be  round 
and  lively,  and  in  a  state  fit  for  grinding ;  being  freed 
from  the  fine  part  that  would  have  prevented  it  from 
feeding  freely.  The  small  specks  of  bran  that  were 
before  mixed  with  it,  being  lighter  than  the  rich  round 

•  Timothy  Kirk,  of  York  Town,  (Pennsylvania,)  has  communicated  to 
me  an  invention  of  his,  an  improved  fun,  for  cleaning  wheal,  the  principle 
of  whrch  is,  to  blow  the  prain  twice  with  one  blast  of  wmd ;  whicli,  with, 
some  further  improvemenis,  appears  lo  offer  fair  to  effect  a  complete  sepa- 
ration of  the  garlic  from  the  wheat,  and  every  other  substance  that  is  light- 
er than  the  grain. 


276  OF  GRINDING  MIDDLINGS,  &c.  [Chap.  4. 

part,  will  not  pass  through  the  middlings'  cloth,  but  will 
pass  on  to  the  stuff's  cloth.  The  middlings  will,  by  this 
means,  be  richer  than  before ;  and  when  made  fine,  may 
be  mixed  with  the  ground  meal,  and  bolted  into  super- 
fine flour. 

The  middlings  may  now  be  put  into  the  hanging 
garner,  over  the  hopper  of  the  stones  ;  out  of  \\  hich  it 
will  run  into  the  hopper,  and  keep  it  full,  as  does  the 
wheat,  provided  the  garner  be  rightly  constructed,  and 
a  hole,  about  6  by  6  inches  made  for  it  to  issue  out  at. 
There  must  be  a  rod  put  through  the  bar  that  supports 
the  upper  end  of  the  damsel,  the  lovier  end  of  which 
must  reach  into  the  eye  of  the  stone,  near  to  the  bottom, 
and  on  one  side  thereof,  to  prevent  the  meal  from  stick- 
ing in  the  eye,  w  hich  if  it  does  it  will  not  feed.  The  hole 
in  the  bottom  of  the  hopper  must  not  be  less  than  four 
inches  square.  Things  being  thus  prepared,  and  the 
stones  being  sharp  and  clean,  and  nicely  hung,  draw  a 
small  quantity  of  water,  (for  meal  does  not  require  above 
one-tenth  part  that  grain  does)  taking  great  care  to  avoid 
pressure,  because  the  bran  is  not  between  the  stones 
now  to  prevent  their  coming  too  close  together.  If  you 
lay  on  as  much  weight  as  when  grinding  grain,  the  flour 
will  be  killed.  But  if  the  stones  be  well  hung,  and  it  be 
pressed  lightly,  the  flour  will  be  lively,  and  will  make 
much  better  bread,  without  being  bolted,  than  it  would 
before  it  was  ground.  As  fast  as  it  is  ground,  it  may  be 
elevated  and  bolted ;  but  a  little  bran  m  ill  now  be  neces- 
sary to  keep  the  cloth  open ;  and  all  that  passes  thnjugh 
the  superfine  cloth  in  this  operation,  may  be  mixed  with 
what  passed  through  in  the  first  bolting  of  the  middlings  : 
and  be  hoisted  up,  and  mixed  (by  the  hopper-boy)  regu- 
larly with  the  ground  meal,  and.  bolted  into  superfine 
flour,  as  directed  art.  89.* 

The  stuff,  which  is  a  degree  coarser  than  middlings, 
if  it .  be  too  poor  for  ship  bread,  and  too  rich  to  feed 

•  But  all  this  trouble  and  loss  of  time  may  be  saved  by  a  little  simple 
machinery  of  late  in\ention,  that  will  cost  but  a  few  dollars,  viz.  As  the 
middlings  fall  by  th.  first  bolting-,  let  them  be  conveyed  into  tlie  eye  of  the 
stone,  and  ground  with  the  wheat,  us  directed  art.  89,  plate  VHI.;  by  which 
means,  the  wliole  thereof  may  be  made  into  snpeifine  flour,  wi'honi  any 
loss  of  time,  or  danger  of  being  too  hard  pressed  for  want  of  the  bran 
to  keep  the  stones  apart.  This  mode  I  first  introduced,  and  several  others 
have  since  adopted  it  with  approbation. 


Chap.  5.]    QUALITY  OF  MILL-STONES,  &c.  Q77 

cattle  on,  is  to  be  ground  over  in  the  same  manner  as 
the  middlings.  But  if  it  be  mixed  with  fine  flour,  (as  it 
sometimes  is,)  so  that  it  will  not  feed  freely,  it  must  be 
bolted  over  first;  this  will  take  out  the  fine  flour,  and 
also  the  fine  specks  of  bran,  which  being  lightest,  will 
come  through  the  cloth  last.  When  it  is  bolted,  the 
part  that  passes  through  the  middlings'  and  stuff''s  parts 
of  the  cloth,  are  to  be  mixed  and  ground  together;  by 
which  means  the  rich  particles  will  be  reduced  to  flour; 
and  w  hen  bolted  will  pass  through  the  finer  cloths,  and 
will  make  tolerable  good  bread.  What  passes  through 
the  middlings'  cloth,  will  make  but  indifferent  ship-bread, 
and  w  hat  passes  through  the  ship-stuff''s  cloth,  will  be 
what  is  called  brown-stuft',  roughings,  or  horse-feed. 

The  bran  and  shorts  seldom  are  worth  the  trouble  of 
grinding  over,  unless  the  stones  have  been  very  dull ;  or 
the  grinding  been  but  slightly  performed ;  or  the  wheat 
very  garlicky.  For  this  purpose  the  stones  are  to  be 
very  sharp,  and  more  water  and  pressure  is  here  required, 
than  in  grinding  grain.  The  flour  that  is  made  there- 
of, is  generally  of  an  indifferent  quality,  being  made  of 
that  part  of  the  grain  that  lies  next  the  skin,  and  great 
part  thereof,  being  the  skin  itself,  cut  fine.* 


CHAPTER  V. 

ART.    414. 

OF  THE  QUALITY  OF  MILL  STONES,  TO  SUIT  THE  QUALITY  OF 
THE  WHEAT. 

IT  has  been  found  by  experience,  that  different  quali- 
ties of  wheat  require  different  qualities  of  stones,  to  grind 
to  the  best  perfection. 

•  But  the  merchant  miller  is  to  consider,  that  there  is  a  certain  degree 
of  closeness  or  perfection  that  he  is  to  aim  at  in  maniifacturini^,  which  will 
yield  him  the  maximum,  or  j^reitest  profit  possihle,  in  a  given  time.  And 
this  degree  of  care  and  perfecion  will  vary  with  the  prict-s  of  wheat  and 
flour,  so  that  what  would  yield  the  greatest  profit  at  one  time,  would  sink 
money  at  another  ;  because,  if  the  difference  of  the  prices  of  wheat  and 
flour  be  but  little,  then  we  must  make  the  grain  yield  the  must  possible, 
to  obtain  any  profit  Bit  if  the  price  of  flour  be  much  above  that  of  the 
wheat,  then  we  had  best  make  the  greatest  despatch,  even  if  we  should 
not  do  it  so  well,  in  order  that  the  greater  quantity  may  be  done  while 


srs  QUALITY  OF  MILL-STQNES,  &c.   [Chap.  S. 

Although  there  be  several  species  of  wheat,  of  differ- 
ent qualities ;  yet  with  respect  to  the  grinding,  we  may 
take  notice  of  but  the  three  following  qualities,  viz. 

1'.  The  dry  and  hard. 

2.  The  damp  and  soft. 

3.  Wheat  that  is  mixed  with  garlic. 
When  the  grain  that  is  to  be  ground  to  dry  and  hard, 


such  as  is  raised  on 


high. 


and  clay  lands;  threshed  in 


other  prices  last ;  whereas,  if  we  were  to  make  such  a  despatch  when  the 
price  of  flour  was  but  little  above  that  of  wheat,  we  would  sink  money. 

A  TABLE 

Showing  the  product  of  a  bushel  of  wheat  of  different  weights  and  quali- 
ties, ascertained  by  experiments  in  grinding  parcels. 


Tail 

Bead 

Screen. 

Weighi 

Super- 

flour & 

st<.flr, 

ings  and 

per 
bushel. 

fine 
flour. 

mid- 
dlings. 

Ship 
Stuff. 

shortS) 
&bran. 

loss  in 
grind- 

Proof, 
lb. 

Quality  of  the  grain- 

lb. 

lb. 

lb. 

lb. 

lb. 

ing, 
lb. 

59,5 

38,5 

3,68 

2,5 

13,1 

1,72 

59,5 

White  wheat  clean. 

59 

40,23 

3,65 

2,12 

12 

1 

59 

Do.   do    well  cleaned. 

60 

38,7 

3,6 

1,61 

8,52 

7,57 

60 

Red  do-  not  well  do- 

61 

39,7 

5,68 

2,4 

9,54^ 

3,68 

61 

White  do    mixt  with 
green  garlic. 

56 

35.81 

5 

1,85 

7,86 

5,48 

56 

White  do.  very  clean. 

59,25 

35,26 

4,4 

1,47 

11,33 

6,79 

59,25 

Red   do.    with    some 
cockle  Stlight  grains. 

If  the  screenings  had  been  accurately  weighed,  and  the  loss  in  weight 
occasioned  by  the  grinding  ascertained,  this  table  would  have  been  more 
interesting.  A  loss  of  weight  does  take  place  bythe  evaporation  of  the  mois- 
ture by  the  heat  of  the  stones  in  the  operation. 

The  author  having  conceived  that  if  a  complete  separation  of  the  skin  of 
the  wheat  from  the  flour  could  be  eff*ected,  and  the  flour  reduced  to  a  suf- 
ficient degree  of  fineness,  it  might  all  pass  for  superfine  flour.  After  hav- 
ing made  the  experiments  in  the  table,  he  made  such  improvements  in  tlie 
manufacture  by  dressing  the  miil-siones  to  grind  smooth,  and  by  means  of 
the  machinery  which  he  invented,  returning  the  middlings  into  the  eye  of 
the  stone»  to  be  ground  over  with  the  wheat,  and  elevating  the  tail  flour  to 
the  hopper-boy  to  be  bolted  over  again,  &c.  &c.  That  in  making  his  last 
2000  barrels  of  superfine  flour  he  left  no  middlings  nor  ship-stuff"  but  what 
was  too  poor  for  any  kind  of  bread,  exceptmg  some  small  quantities  «  hich 
were  retained  in  the  mill,  and  the  flour  passed  the  inspection  with  credit. 
Others  have  since  pursued  the  same  prmciples  and  put  them  more  fully  and 
completely  in  operation.  Thus  the  manufacture  of  flour  has  arrived  nearly 
to  a  state  of  perfection,  and  those  millers  who  had  faith  to  believe,  have 
for  fourteen  years  past  been  enjoying  themselves,  seeing  the  machinery  of 
their  mills  perform  all  the  laborious  parts  of  the  work,  and  have  been  sell- 
ing and  eating  good  superfine  flour ;  while  those  who  had  not,  have  been 
toiling,  sweating,  and  doing  the  labour  that  the  power  of  the  water  which 
move's  their  mills  might  have  done,  and  have  been  selling  and  eating  mid- 
dlings and  ship-stuff". 


Chap.  5.]     QUALITY  OF  MILL-STONES,  &c.  279 

barns,  and  kept  dry  ;*  the  stones  for  grinding  such 
wheat,  should  be  of  that  quahty  of  the  burr,  that  is  call- 
ed close  and  hard,  with  few  large  pores ;  in  order  that 
they  may  have  more  face.  The  grain  being  brittle  and 
easy  broken  into  pieces,  requires  more  face  or  plane 
parts  (spoken  of  in  art.  104,)  to  reduce  it  to  the  requir- 
ed fineness,  without  cutting  the  skin  too  much. 

When  the  grain  that  is  to  be  ground  is  a  little  damp 
and  soft,  such  as  is  raised  on  a  light,  sandy  soil,  tread 
out  on  the  ground,  and  carried  in  the  holds  of  ships  to 
market,  which  tends  to  increase  the  dampness,  the 
stones  are  required  to  be  more  open,  porous,  and  sharp, 
because  the  grain  is  tough,  difficult  to  be  broke  into 
pieces,  and  requires  more  sharpness,  and  less  face  (or 
plane  surface)  to  reduce  it  to  the  required  fineness. f 
See  art.  104. 

When  there  is  more  or  less  of  the  garlic,  or  wild 
onion,  (mentioned  art.  111.)  mixed  with  the  wheat,  the 
stones  will  require  to  be  open,  porous  and  sharp ;  be- 
cause the  glutinous  substance  of  the  garlic  adheres  to 
the  face  of  the  stones,  and  blunts  the  edges ;  by  which 
means  little  can  be  ground,  before  the  stones  get  so  dull 
that  they  will  require  to  be  taken  up,  and  sharpened ; 
and  the  more  porous  and  sharp  the  stones  are,  the  longer 
will  they  run,  and  the  more  will  they  grind,  without 
getting  dull.  There  is  a  quality  of  the  burr  stone  which 
I  shall  for  distinction  call  a  mellow  or  soft  qualit}%  very 
diiferent  from  the  hard  and  flinty  ;  these  are  not  so  sub- 
ject to  glaze  on  their  face,  and  it  is  found  by  experience 
that  stones   of   this  quality  will  grind  at  one  dressing 

*  Such  wheat  as  is  produced  by  the  mountainous  and  clay  lands  of  the 
country  distant  from  the  sea  and  tide  waters,  is  jjenerally  of  a  brownish 
colour,  the  grain  appearing  flinty,  and  sometimes  the  inside  a  little  trans- 
parent, when  cut  by  a  sharp  knife.  This  transparent  kmd  of  wheat  is  ge- 
nerally heavy,  and  of  a  thin  skin,  and  will  make  as  white  flour,  and  as  much 
of  it,  as  the  whitest  grain. 

f  Such  is  the  wheat  thai  is  raised  in  all  the  low,  level,  and  sandy  lands, 
of  countries  near  the  sea  and  tide  waters  of  America,  where  it  is  customa- 
ry to  tread  out  their  wheat  on  the  ground  by  horses,  and  if  sometimes  gets 
wet  by  rain  and  dew,  and  the  dampness  of  the  ground-  This  grain  is  na- 
turally of  af  a  irer  colour,  and  softer  ;  and  when  bioken,  the  inside  is  white, 
which  siiows  ii  to  be  nearer  a  state  of  pulverisation,  and  is  more  easily  re- 
duced to  flour,  and  will  not  bear  as  mu'h  prrssure  as  the  grain  that  is 
raised  on  high  and  clay  lands,  or  such,  thatwh^n  broken,  appears  solid  and 
transparent 


280    OF  BOLTING-REELS  AND  CLOTHS.    [Chap.  6. 

three  or  four  times  as  much  grain,  mixed  with  garlic,  as 
those  of  a  hard  quahty.*     See  art.  111. 


CHAPTER  VI. 

ART.    115. 

OP  BOLTIKG -REELS,  AND  CLOTHS  ;  WITH  DIRECTIONS  FOR 
BOLIING  AND  INSPECTING  THE  FLOUR- 

THE  effect  we  wish  to  produce  by  sifting,  or  bolting, 
is  to  separate  the  different  qualities  of  flour  from  each 
other ;  and  from  the  skin,  shorts,  or  bran.  For  this  rea- 
son, let  us  consider  the  most  rational  means  that  we  can 
use  to  attain  this  end. 

Queries  concerning  Bolting. 

1.  Suppose  that  we  try  a  sieve,  the  meshes  of  which 
are  so  large,  as  to  let  all  the  bran  and  meal  through  : 
now  it  is  evident,  that  we  could  never  attain  the  end 
proposed  by  the  use  thereof. 

2.  Suppose  we  try  a  finer  sieve,  that  will  let  all  the 

*  It  is  very  difficult  to  convey  my  ideas  of  the  quality  of  the  stones  to 
the  reader,  for  want  of  something  to  measure  or  compare  their  degree  of 
porosity  or  closeness,  hardness  or  softness  with-  The  knowledge  of  these 
diffc-reni  qualities  is  only  to  be  attained  by  practice  and  experience;  hut  I 
m..y  observe,  that  there  is  no  need  of  any  pores  in  the  stone  to  be  larger  in 
diameter  than  the  length  of  a  grain  of  wheat,  for  whatever  they  are  larger, 
is  so  much  loss  of  the  face,  because  it  is  the  edges  that  do  the  grinding; 
thert- f  )re,  all  larjije  pores  in  stones  are  a  disadvantage.  The  greater  the 
number  of  pores  in  the  stone,  (so  as  to  leave  a  sufficient  quantity  of  touch- 
ing surfaces,  to  reduce  the  flour  to  a  sufficient  degree  of  fineness)  the  bet- 
ter. 

Mill-stone  makers  ought  to  be  acquainted  with  the  true  principles  on 
which  grinding  is  perform<-d,  and  with  the  art  of  manufacturing  grain  into 
flour,  that  they  may  be  judges  of  the  quality  of  the  stones  suitable  to  the 
quality  of  the  wheat,  of  different  parts  of  the  country;  also,  of  the  best 
manner  of  disposing  of  the  different  pieces  of  stone,  of  different  qualities, 
in  the  same  mill  si  one,  according  to  the  office  of  the  several  parts,  from  the 
centre  to  the  verge  of  the  stone.     See  art-  104- 

Mill  stones  are  generally  but  very  carelessly  and  slightly  made,  whereas, 
they  should  be  made  with  the  greatest  care  and  to  the  greatest  nicety.  The 
ri'nner  must  be  balanced  exactly  on  its  centre,  and  every  corresponding 
opposite  part  of  it  shouhl  be  of  equal  weight,  or  else  the  spindle  will  not 
keep  tight  m  the  bush  :  (see  art.  107)  and  if  it  is  to  be  hung  on  a  balance 
ryne,  it  should  be  put  in  at  the  formation  of  the  stone,  which  should  be 
oicely  balanced  thereon. 

But  above  all,  the  q>alityof  the  stone  should  be  most  attended  to,  that 
no  piece  of  un  unsuitable  quality  for  the  rest,  be  put  in ;  it  being  known  to 
mos  experienced  millers,  that  they  had  better  give  a  high  price  for  an  ex- 
traordinary good  pair,  than  to  have  an  indifferent  pair  for  nothing. 


Chap.  6.]  OF  BOLTING-KEELS  AND  CLOTHS.  281 

meal  through,  but  none  of  the  bran  :  but  by  this  we  can- 
not separate  the  different  qualities  of  flour. 

3.  We  provide  as  many  sieves  of  the  different  degrees 
of  fineness,  as  we  intend  to  make  different  qualities  of 
flour ;  and  which,  for  distinction,  we  name — Superfine, 
Middlings,  and  Carnel. 

The  superfine  sieve,  of  meshes  so  fine  as  to  let  through 
the  superfine  flour,  but  none  of  the  middlings  :  the  mid- 
dlings' sieve,  so  fine  as  to  let  the  middlings  pass  through, 
but  none  of  the  camel :  the  carnel  sieve,  so  fine  as  to  let 
none  of  the  shorts  or  bran  pass  through. 

Now  it  is  evident,  that  if  we  would  continue  the  ope- 
ration long  enough,  with  each  sieve,  beginning  with  the 
superfine,  that  we  might  effect  a  complete  separation.* 
But  if  we  do  not  continue  the  operation  a  sufficient  length 
of  time,  with  each  sieve,  the  separation  will  not  be  com- 
plete. For  part  of  the  superfine  will  be  left,  and  will 
pass  through  with  the  middlings,  and  part  of  the  mid- 
dlings with  the  carnel,  and  part  of  the  carnel  with  the 
shorts ;  and  this  would  be  a  laborious  and  tedious  work, 
if  performed  by  the  hand. 

To  facilitate  this  business,  many  have  been  the  im- 
provements ;  amongst  which  the  circular  sieve,  or  bolt- 
ing-reel, is  one  of  the  foremost ;  and  which  was,  at  first, 
turned  and  fed  by  hand ;  though  afterwards  contrived 
to  be  turned  by  water. 

But  many  have  been  the  errors  in  the  application  of 
this  machine,  either  by  having  the  cloths  too  coarse,  by 
which  means  the  middlings  and  small  pieces  of  bran  will 
pass  through  with  the  superfine  flour,  and  part  of  the 
carnel  with  the  middlings  :  or  by  having  the  cloths  too 
short,  when  they  are  fine  enough,  so  that  the  operation 
cannot  be  continued  a  sufficient  time  to  take  all  the 
superfine  out,  before  it  reaches  the  middlings'  cloth,  and 
all  the  middlings,  before  it  reaches  the  carnel  cloth. 

The  late  improvements  made  on  bolting,  seem  to  be 
wholly  as  follows,  viz. 

•  This  metUod  I  have  been  informed  is  practised  in  England  ;  they  have 
several  bolting^  cloths  of  difFereni  degrees  of  fineness  for  the  same  ivel. 
They  first  put  on  the  fine  one,  and  piss  the  meal  chrout^h.  whi  h  taktrs  out 
the  superfine  flour;  they  then  take  off  ihe  superfine  cloth,  md  put  on  'he 
next  degree  of  fineness,  which  takes  out  the  common  fin  •  floup;  and  so  on 
through  the  lifferent  <legTees,  the  cloths  having  drawl ng-strings  at  each  end 
for  drawing  the  ends  close. 

N  n 


282  OF  INSPECTING  FLOUR.         [Chap.  6, 

1.  By  using  finer  cloths — but  they  were  found  to 
clog,  or  choke  up,  when  put  on  small  reels  of  22  inches 
diameter. 

S.  By  enlarging  the  diameter  of  the  reels  to  271 
inches,  which  gives  the  meal  greater  distance  to  fall,  and 
causes  it  to  strike  harder  against  the  cloth,  which  keeps 
it  open. 

3.  By  lengthening  the  cloths,  that  the  operation  may 
be  continued  a  sufficient  length  of  time. 

4.  By  bolting  a  greater  part  of  the  flour  over  again, 
than  was  done  formerly. 

The  meal,  as  it  is  ground,  must  be  hoisted  to  the  meal- 
loft,  where  it  is  spread  thin,  and  often  stirred,  that  it  may 
cool  and  dry,  to  prepare  it  for  bolting.  After  it  is  bolted, 
the  tail-flour,  or  that  part  of  the  superfine  that  falls  last, 
and  which  is  too  full  of  specks  of  bran  to  pass  for  super- 
fine flour,  is  to  be  hoisted  up  again,  and  mixed  with  the 
ground  meal,  to  be  bolted  over  again.  This  hoisting, 
spreading,  mixing,  and  attending  the  bolting  hoppers,  in 
merchant- mills,  creates  a  great  deal  of  hard  labour,  if 
done  by  hand ;  and  is  never  completely  done  at  last :  but 
all  this,  and  much  more  of  the  labour  of  mills,  can  now 
be  done  by  machinery,  moved  by  water.  See  part.  3. 
Of  Inspecting  Flour. 

The  miller  must  by  some  means  attain  a  knowledge 
of  the  standard  quality,  passable  in  the  markets. 

He  holds  a  clean  piece  of  board  under  the  bolt,  mov- 
ing it  from  head  to  tail,  so  as  to  catch  a  proportional 
quantity  all  the  way,  as  far  as  is  taken  for  superfine  :  then, 
having  smoothed  it  well,  by  pressing  an  even  surface  on 
it,  to  make  the  specks  and  colour  more  plainly  appear ; 
if  it  be  not  good  enough,  turn  a  little  more  of  the  tail  to 
to  be  bolted  over. 

If  the  flour  appears  darker  than  expected,  from  the 
quality  of  the  grain,  it  shows  the  grinding  to  be  high, 
and  bolting  too  near ;  because  the  finer  the  flour,  the 
whiter  its  colour.* 

*  This  appears  reasonable,  when  we  consider,  that  many  dark  coloured 
and  transparent  substances  (while  in  a  solid  state)  when  pulverised,  be- 
come white,  and  their  whiteness  is  proportionate  to  the  dei^ree  of  pulveri- 
sation ;  for  instance,  salt,  alum,  and  many  kinds  of  stone,  and  particularly 
slate. — Ice  pulverised  is  as  white  as  snow,  transparent  wheat  makes  the 
whitest  flour. 


Chap.  7.]  THE  MILLER'S  DUTY.  283 

But  this  mode  requires  good  light ;  therefore,  the  best 
way  is  for  the  miller  to  observe  to  what  degree  of  poor- 
ness he  may  reduce  his  tail  Hour,  or  middlings,  so  as  to 
be  safe ;  by  which  he  may  judge  with  much  more  safety 
in  the  night.  But  the  quality  of  the  tail  flour,  middlings, 
&:c.  will  gready  vary  in  different  mills ;  for  those  that 
have  the  late  improvements  for  bolting  over  the  tail  flour, 
grinding  over  the  middlings,  &c.  can  make  nearly  all 
into  superfine. 

Whereas,  those  that  have  them  not — the  quality  that 
remains  next  to  superfine,  is  common,  or  fine  flour ;  then 
rich  middlings,  ship-stuff,  &c.  Those  who  have  expe- 
rience will  conceive  the  difference  in  the  profits.  If  the 
flour  feels  soft,  dead,  and  oily,  yet  white,  it  shows  the 
stones  to  have  been  dull,  and  too  much  pressure  used.  If 
it  appear  li\'ely,  yet  dark  coloured,  and  too  full  of  very 
fine  specks,  it  shows  the  stones  to  have  been  too  rough, 
sharp,  and  that  it  was  ground  high  and  bolted  too  close. 


CHAPTER  VIL 

Directions  for  keeping  the  Mill^  and  the  business  of  it^  in 
good  order. 


ART.    116. 

THE  DUTY  OF  THE  MILLER. 

THE  mill  is  supposed  to  be  completely  finished  for 
merchant  work,  on  the  new  plan ;  supplied  with  a  stock  of 
grain,  flour  casks,  nails,  brushes,  picks,  shovels,  scales, 
weights,  &c.  when  the  millers  enter  on  their  duty. 

If  there  be  two  of  them  capable  of  standing  watch,  or 
taking  charge  of  the  mill,  the  time  is  generally  divided 
as  follows  :  In  the  day  time  they  both  attend  to  business, 
but  one  of  them  has  the  chief  direction  :  The  night  is 
divided  into  two  watches,  the  first  of  which  ends  at  one 
o'clock  in  the  morning  ;  when  the  master  miller  should 
enter  on  his  watch,  and  continue  till  morning ;  that  he 
may  be  ready  to  direct  other  hands  to  their  business 
early.  The  first  thing  he  should  do,  when  his  watch 
begins,  is  to  see  whether  the  stones  are  grinding-,  and  the 
cloths  bolting,  well. 


284  THE  MILLER'S  DUTY.  [Chap.  7. 

And  2dly,  to  review  all  the  moving  gudgeons  of  the 
mill,  to  see  whether  any  of  them  want  grease,  Sslc.  that 
he  may  know  what  care  may  be  necessary  for  them  dur- 
ing his  watch  ;  for  want  of  this  the  gudgeons  often  run 
dry,  and  heat,  which  brings  on  heavy  losses  of  time  and 
repairs ;  for  when  they  heat,  they  get  a  little  loose,  and 
the  stones  they  run  on  crack,  after  which  they  cannot  be 
kept  cool.  He  should  also  see  what  quantity  of  grain  is 
over  the  stones,  and  if  there  be  not  enough  to  supply 
them  till  morning,  set  the  cleaning  machines  in  motion. 

All  things  being  set  right,  his  duty  is  very  easy — he 
has  only  to  see  the  machinery,  the  grinding,  and  bolting, 
once  in  an  hour;  he  has  therefore  plenty  of  time  to 
amuse  himself  in  reading.  Sec.  rather  than  going  to 
sleep,  which  is  not  safe. 

Early  in  the  morning,  all  the  floors  should  be  swept, 
and  the  flour  dust  collected.  The  casks  nailed,  weighed, 
marked  and  branded,  and  the  packing  began,  that  it  may 
be  completed  in  the  forepart  of  the  day  ;  by  this  means, 
should  any  unforeseen  thing  occur,  there  will  be  spare 
time.  Besides,  to  leave  the  packing  till  the  afternoon, 
is  a  lazy  practice,  and  keeps  the  business  out  of  order. 

When  the  stones  are  to  be  sharpened,  every  thing 
necessary  should  be  prepared  before  the  mill  is  stopped, 
(especially  if  there  be  but  one  pair  of  stones  to  a  water- 
wheel)  that  as  little  time  as  possible  may  be  lost :  the 
picks  made  right  sharp,  not  less  than  12  in  number. 
Things  being  ready,  take  up  the  stone  ;  set  one  hand  to 
each,  and  dress  them  as  soon  as  possible,  that  they  may 
be  set  to  work  again  ,  not  forgetting  to  grease  the  gears, 
and  spindle  foot. 

In  die  after  part  of  the  day,  a  sufficient  quantity  of  grain 
is  cleaned  down,  to  supply  the  stones  the  whole  night ; 
because  it  is  best  to  have  nothing  to  do  in  the  night,  more 
than  to  attend  to  the  grinding,  bolting,  gudgeons,  &c. 


ART.    117. 

PECULIAR   ACCIDENTS    BY   WFUCH    MILLS   ARE    SUBJECT   TO 
CATCH  FIRE. 

1.  There  being  many  moving  parts  in  a  mill,  if  any 
piece  of  timber  fall,  and  lay  on  any  moving  wheel,  or 


Chap.7.]     ON  IMPROVING  OF  MILL-SEATS.      285 

shaft,  and  the  velocity  and  pressure  be  great,  it  will  ge- 
nerate fire,  and  perhaps  consume  the  mill. 

S.  Many  people  use  wooden  candlesticks,  that  may  be 
set  on  a  cask,  bench,  or  the  floor,  and  forgetting  them,  the 
candle  bums  down,  sets  the  stick,  cask,  &c.  on  fire,  which 
perhaps  may  not  be  seen  until  the  mill  is  in  a  flame. 

3.  Careless  millers  sometimes  stick  a  candle  to  a  cask, 
or  post,  and  forget  it,  until  it  burns  a  hole  in  the  post,  or 
sets  the  cask  on  fire. 

4.  Great  quantities  of  grain  sometimes  bend  the  floor 
so  as  to  press  the  head  blocks  against  the  top  of  the 
upright  shafts,  and  generate  fire :  (unless  the  head  blocks 
have  room  to  rise  as  the  floor  settles)  mill-wrights  should 
consider  this,  and  be  careful  to  guard  against  it  as  they 
build. 

5.  Branding  irons,  carelessly  laid  down,  when  hot, 
and  left,  might  set  something  on  fire. 

6.  I  have  heard  of  bran  falling  from  the  tail  of  a  bolt, 
round  a  shaft,  the  friction  of  which  burnt  the  shaft  off". 

7.  The  foot  of  the  mill-stone  spindle,  and  gudgeons, 
frequently  heat,  and  set  the  bridge- tree  or  shaft  on  fire. 
It  is  probable,  that  from  such  causes  mills  have  taken 
fire,  when  no  person  could  discover  how. 


ART.    118. 

OBSERVATIONS    ON  IMPROVING  OF  MILL  SEATS. 

I  may  end  this  part  with  a  few  observations  on  im- 
proving mill- seats.  The  improving  of  a  mill-seat  at 
1000/.  expense,  is  an  undertaking  worthy  of  mature  de- 
liberation, as  wrong  steps  may  increase  it  to  1100/.  and 
the  improvement  be  incomplete:  whereas,  right  steps 
may  reduce  it  to  900/.  and  perfect  them. 

Strange  as  it  may  appear,  yet  it  is  a  real  fact,  that  those 
who  have  least  experience  in  the  milling  business,  gene- 
rally build  the  best  and  completest  mills.  The  reasons 
are  evident — 

The  experienced  man  is  bound  to  old  systems;  he  re- 
lies on  his  own  judgment  in  laying  all  his  plans;  whereas. 

The  unexperienced  man,  being  conscious  of  his  defi- 
ciency, is  at  liberty;  perfectly  free  from  all  prejudice, 
to  call  on  all  his  experienced  friends,  and  to  collect  all 
the  improvements  that  are  extant. 


286        ON  IMPROVING  OF  MILL-SEATS.  [Chap.r. 

A  merchant  who  knows  but  little  of  the  miller's  ait, 
or  of  the  structure  or  mechanism  of  mills,  is  naturally 
led  to  the  following  steps,  viz. 

He  calls  several  of  the  most  experienced  millers  and 
mill-wrights,  to  view  the  seat  separately,  and  point  out 
the  spot  for  the  mill-house,  dam,  &c.  and  notes  their 
reasonings  in  favour  of  their  opinion.  The  first  perhaps 
fixes  on  a  pretty  level  spot  for  the  mill-house,  and  a  cer- 
tain rock,  that  nature  seems  to  have  prepared,  to  support 
the  breast  of  the  dam,  and  an  easy  place  to  dig  the  race, 
mill-seat,  &c. 

The  second  passes  by  these  places  without  noticing 
them ;  explores  the  stream  to  the  boundary  line ;  fixes  on 
another  place,  the  only  one  he  thinks  appointed  by  nature 
for  building  a  lasting  dam,  the  foundation  a  solid  rock, 
that  cannot  be  undermined  by  the  tumbling  water;  fixing 
on  a  rugged  spot  for  the  seat  of  the  house :  assigning  for 
his  reasons,  that  the  whole  fall  must  be  taken  in,  that  all 
may  be  right  at  a  future  day.  He  is  then  informed  of  the 
opinion  of  the  other,  against  which  he  gives  substantial 
reasons. 

The  mill-wright,  carpenter  and  mason,  that  are  to  un- 
dertake the  building,  are  now  called  together,  to  view  the 
seat,  fix  on  the  spot  for  the  house,  dam,  &c.  After  their 
opinion  and  reasons  are  heard,  they  are  informed  of  the 
opinion  and  reasons  of  the  others,  all  are  joined  together, 
and  the  places  are  fixed  on.  They  are  then  desired  to 
make  out  a  complete  draught  of  the  plan  for  the  house, 
&c.  and  to  spare  no  pains  to  plan  all  for  the  best ;  but 
alter  and  improve  on  paper,  till  all  appear  to  meet  right, 
in  the  simplest  and  most  convenient  manner;  (a  week 
may  be  thus  well  spent)  making  out  complete  bills  of 
every  piece  of  timber,  quantity  of  boards,  stone,  lime, 
&c.  bill  of  iron  work,  number  of  wheels,  their  diame- 
ters, number  of  cogs,  &c.  &c.  in  the  whole  work.  Each 
person  can  then  make  out  his  charge,  and  the  costs  can 
be  counted  nearly.  Every  species  of  materials  may  be 
contracted  for,  to  be  delivered  in  due  time :  then  the 
'  work  goes  on  regularly  without  disappointment,  and  when 
done,  the  improvements  are  complete,  and  100/.  out  of 
1000/.  at  least  saved  by  such  steps. 


PART  V. 

THE 

PRACTICAL  MILL-WRIGHT; 

CONTAIlSriNG 

INSTRUCTIONS  FOR  BUILDING  MILLS, 

WITH 

ALL  THEIR  PROPORTIONS  j 

SUITABLE 

TO  ALL  FJLLS  OF  FROM  THREE  TO  THIRTY-SIX  FEET. 


Received  from  Thomas  Ellicott, 

Mill-fVright. 


CONTENTS  OF  PART  V. 


T^he  Preface  explains  the  Plate  containing  the  new  im- 
provements. 

ART.  1.  Of  undershot  mills — directions  for  laying  on 
the  water. 

Art.  2.  Draught  of  a  forebay,  with  directions  for  mak- 
ing them  durable. 

Art.  3.  Principles  and  practical  experiments,  to  deter- 
mine the  proper  motion  for  undershot  wheels. 

A  table  for  gearing  undershot  wheels,  suited  to  all  falls, 
from  3  to  20  feet. 

Art.  4.  Of  breast  mills,  with  directions  for  proportioning 
and  gearing  them,  to  give  the  stone  the  right  motion. 

Art.  5.  Of  pitch-back  mills,         do.         do. 

Art.  6.  Of  overshot  mills,  and  their  dimensions. 

Art.  7.  Of  the  proper  motion  for  overshot  mills. 

Art.  8.  Of  gearing  the  water-wheel  to  the  mill-stones, 
to  give  them  the  proper  motion. 

Art.  9.  Rules  for  finding  the  diameter  of  the  pitch  circles. 

Table  of  all  the  proportions  for  overshot  mills,  suitable 
for  all  falls,  from  15  to  36  feet ;  for  4  and  4;  feet  6 
inches,  and  5  and  5  feet  6  inch  stones,  diameter. 

Art.  10.  Directions  for  constructing  undershot  wheels, 
for  dressing  shafts. 
,  for  laying  out  mortises  for  arms, 
for  putting  in  gudgeons, 
for  constructing  cog-wheels, 
for  making  sills,   spurs,  and  head 
blocks. 

Art.  16.  Of  the  best  time  for  cutting  cogs,  and  method 
of  seasoning  them. 

Art.  17.  Of  shanking,  putting  in,  and  dressing  off  the 
cogs. 

Art.  18.  Of  the  little  cog-wheel  and  shaft. 

0  o 


Art. 

11. 

do. 

Art. 

12. 

do. 

Art. 

13. 

do. 

Art. 

14. 

do. 

Art. 

15. 

do. 

a90  CONTENTS. 

Art.  19.  Directions  for  making  wallowers  and  trundles. 

Art.  20.  do.  for  fixing  the  head  blocks,  and  hang- 
ing the  wheels. 

Art.  21.  Directions  for  sinking  the  balance  ryne. 

Art.  22.         do.        for  bridging  the  spindle. 

Art.  S3.  do.  for  making  the  crane  and  lighter- 
staff. 

Art.  24.  do.  for  making  a  hoop  for  the  mill- 
stones. 

Art.  25.         do.        for  grinding  sand  to  face  the  stones. 

Art.  26.  do.  for  laying  out  the  furrows  in  new 
stones. 

Art.  27.         do.        for  making  a  hopper,  shoe  and  feeder. 

Art.  28.         do.        for  making  bolting  chests  and  reels. 

Art.  29.         do.        for  setting  bolts  to  go  by  water. 

Art.  30.         do.        for  making  bolting  wheels. 

Art.  31.  or  roUing-screens. 

Art.  S2  OF  fans. 

Art.  33.  Of  the  shaking  sieve. 

Art.  34.  Of  the  use  of  draughting  to  build  mills  by. 

Art.  35.  Directions  for  draughting  and  planning  mills. 

Art.  36.  Bills  of  bcanding  for  a  mill. 

Art.  37.  Bills  of  iron  work  for  do. 

Art.  38.  Explanation  of  the  plates. 

Art.  39.  Of  saw- mills,  with  a  table  of  the  dimensions  of 
flutter-wheels,  to  suit  all  heads  from  6  to  30  feet. 

Art.  40.  Of  fulling-mills. 


TO  THE  READER. 


I  BEING  requested  by  Oliver  Evans,  to  assist 
iiim  in  completing  his  book,  entitled,  The  Young 
Mill- Wright  and  Miller's  Guide,  have  thought  pro- 
per to  give  the  reader  a  short  history  of  the  rise 
and  progress  of  merchant  mills,  towards  their  pre- 
sent state  of  perfection,  since  the  beginning  of  my 
time. 

It  is  now  upwards  of  38  years  since  I  first  be- 
gan mill-wrighting:  I  followed  it  very  constantly  for 
about  ten  years,  making  it  niy  particular  study. 
Several  of  my  brothers  being  also  mill-wrights,  we 
kept  in  company,  and  were  often  called  to  different 
parts  of  this  and  the  adjacent  states,  to  build  mills 
of  the  first  rates,  in  their  day.  Some  of  them  en- 
tered into  the  manufacturing  line;  but  I  continued 
at  mill-wrighting,  and  other  business  connected 
therewith ;  such  as  roUing-screens,  and  fans,  and 
making  them  to  go  by  water,  in  merchant  and 
grist-mills ;  also  farmer's  fans,  for  cleaning  grainy 
being  one  of*  the  first,  1  believe,  that  made  these 

•  .Mr-  Ellicolt  observed  that  he  was  sorry  the  words  (one  of)  hftU  been 
left  out,  therefore  they  were  put  in  by  Mr.  Rvans. 


:29a  TO   THE  READER. 

things  in  America:  but  for  several  years  past, 
have  done  but  little  else  than  build  mills,  or 
draught  to  build  by. 

When  I  first  began  the  business,  mills  were  at 
a  low  ebb  in  this  country ;  neither  burr-stones, 
nor  rolling-screens  being  used ;  and  but  few  of 
the  best  merchant  mills  had  a  fan.  Many  carried 
the  meal  on  their  backs,  and  bolted  it  by  hand, 
even  for  merchant  work ;  and  I  have  frequent- 
ly heard,  that  a  little  before  my  beginning  the 
business,  it  had  been  customary,  in  many  in- 
stances, to  have  the  bolting  mill  some  distance 
from  the  grinding  mill,  and  there  bolted  by  hand. 
It  was  counted  extraordinary  when  they  got  their 
bolting  to  go  by  water :  after  this,  fans  by  hand, 
and  standing-screens,  took  place;  then  burr-stones, 
rolling-screens,  and  superfine  bolting  cloths,  with 
a  nuniber  of  other  improvements.  Some  of  the 
latest  are,  the  elevators,  hopper-boys,  ^c;  invent- 
ed by  Oliver  Evans,  late  of  Delaware,  though  now 
of  Philadelphia. 

Being  very  desirous  to  improve  in  the  art  of 
building  mills,  and  manufacturing  grain  into  flour, 
I  have  frequently  went  a  considerable  distance  to 
see  new  improvements,  and  have  often  searched 
the  book-stores  in  expectation  of  finding  books 
that  might  instruct  me,  but  never  found  any  which 
was  of  use  to  me  in  that  respect,  more  than  to 
learn  the  ancient  names  of  some  parts  of  the  mills; 
for  although  they  had  been  wrote  by  men  of  con- 
siderable learnicg,  in  other  respects ;  yet,  as  they 


TO  THE  READER.  S93 

had  never  been  mill-wrights  themselves,  they  had 
neither  practical,  nor  experimental  knowledge  to 
direct  them  in  the  work.  For  instance,  see  the 
mill-wright's  table,  in  Ferguson's  Lectures,  page 
79^  where  the  cog-wheel  is  to  have  i27  cogs, 
about  15  i-2  feet  diameter;  trundle,  6  staves,  and 
stones  6  feet:  And  in  Imison's  Introduction  to 
Useful  Knowledge,  page  31,  the  water-wheel  is  to 
be  18  feet,  cog-wheel  S54  cogs,  about  31  feet  di- 
ameter, much  higher  tlian  the  water-wheel ;  staves 
in  the  trundle  (5,  and  stones  4  l-S  feet.  Besides^ 
some  liave  asserted,  that  water  applied  on  an  un- 
dershot wheel,  will  do  6  times  as  much  as  if  ap- 
plied on  an  overshot ;  others,  that  if  apphed  on  an 
overshot  it  will  do  10  times  as  much  as  an  under- 
shot, the  quantity  and  falls  being  equal ;  many 
other  parts  of  their  theories  are  equally  wrong 
in  practice.  So  that  what  knowledge  I  have  gain- 
ed, has  been  by  steady  attention  to  the  improve- 
ments of  our  own  country :  I  have  wondered,  that 
no  person  of  practical  knowledge  in  the  art,  has 
yet  attempted  to  write  a  treatise  on  it,  seeing  it  is 
a  subject  worthy  attention,  and  such  a  book  so 
much  wanted.  The  manufacturing  of  our  own 
country  produce,  in  the  most  saving,  expeditious, 
and  best  manner,  I  have  thought,  is  a  subject  wor- 
thv  the  attention  of  the  legislatures.  Mills  are 
often  laid  under  heavy  taxes,  being  supposed  to 
be  very  profitable  ;  but  if  all  the  spare  wheat  was 
to  be  shipped,  where  would  the  miller's  profit  be? 
But  to  return  to  the  subject :  I  have  often  thought, 


S94  TO  THE  READER. 

that  if  I  could  spare  time,  I  would  write  a  small 
treatise  on  mill-wrighting  myself,  (thinking  it  would 
be  of  much  use  to  young  mill-wrights,)  but  fearing 
I  was  not  equal  to  the  task,  I  was  ready  to  give  it 
up;  but  on  further  consideration,  I  called  on  Tho- 
mas Dobson,  printer  of  the  Encyclopedia,  and  ask- 
ed him  if  he  would  accept  of  a  small  treatise  on 
mill-wrighting;  he  said  Oliver  Evans  had  been 
there  a  few  days  before,  and  proposed  such  a 
work,  which  1  thought  would  save  me  the  trouble. 
But  some  time  afterwards,  the  said  Evans,  apphed 
to  me,  requesting  my  assistance  in  his  under- 
taking ;  this  I  was  the  more  willing  to  do,  having 
built  several  mills  with  his  additional  improve- 
ments, and  draughted  several  others ;  and  without 
which  improvements,  I  think  a  mill  cannot  now 
be  said  to  be  complete.  By  them  the  manufac- 
ture of  grain  into  flour,  is  carried  on  by  water 
with  very  little  hand  labour,  and  much  less  waste, 
either  in  small  or  large  business.  And  I  do  be- 
lieve, that  taking  a  large  quantity  of  wheat  toge- 
ther, that  we  can  make  2  or  3  lbs.  more  out  of  a 
bushel  by  the  new,  than  by  the  old  way,  although 
ft  be  equally  well  ground ;  because  it  is  so  much 
more  completely  bolted,  and  v/ith  less  waste.  In 
the  old  way,  the  wheat  is  weighed  and  carried  up 
one  or  two  pair  of  stairs,  and  thrown  into  garners j 
the  bags  often  having  holes  in,  it  is  spilt  and  tram- 
pled under  foot ;  several  pounds  being  frequently 
lost  in  receiving  a  small  quantity ;  and  when  it  is 
taken  from  these  garners,  and  carried  to  the  roll- 


TO  THE  READER.  S95 

iiig-screens,  some  is  again  wasted,  and  as  it  is 
ground,  it  is  shoveled  into  tubs,  a  dust  is  raised, 
and  some  spilt  and  trampled  on ;  it  is  then  hoist- 
ed, and  spread,  and  tossed  about  with  shovels,  over 
a  large  floor,  raked  and  turned  to  cool,  and  shov- 
eled up  again,  and  put  into  the  bolting  hopper ;  all 
which  occasions  great  labour,  besides  being  spilt 
and  trampled  over  the  mill,  which  occasions  a  con- 
siderable waste.  Besides  these  disadvantages, 
there  are  others  in  attending  the  bolting  hoppers ; 
being  often  let  run  empty,  then  filled  too  hard, 
so  that  they  choke,  which  occasions  the  flour  to  be 
very  unevenly  bolted ;  sometimes  too  poor,  and 
at  other  times  too  rich,  which  is  a  considerable 
loss  ;  and  when  the  flour  is  bolted,  it  is  much 
finer  at  the  head  than  tiie  tail  of  the  cloths ;  the 
fine  goes  through  first,  and  has  to  be  mixed  by 
hand,  with  shovels  or  rakes ;  and  this  labour  is 
often  neglected  or  only  half  done  ;  by  this  means, 
part  of  the  flour  will  be  condemned  for  being  too 
poor,  and  the  rest  above  the  standard  quality. 
The  hoisting  of  the  tail  flour,  mixing  it  with  bran, 
by  hand,  and  bolting  it  over,  is  attended  with  so 
much  labour,  that  it  is  seldom  done  to  perfection. 
In  the  new  way,  all  these  inconveniences  and 
disadvantages  are  completely  provided  against : 
See  plate  XXII ;  which  is  a  representation  of  the 
machinery,  as  they  are  applied  in  the  whole  pro- 
cess of  the  manufacture,  taking  the  grain  from  the 
ship  or  wagon,  and  passing  it  through  the  whole 
process  by  water,  until  it  is  completely  manufac- 
tured into  superfine  flour.    As  they  are  applied 


^96  TO   THE   READElt. 

in  a  mill  of  my  planning  and  draughting,  now  in 
actual  practice,  built  on  Occoquam  river,  in  Virgi- 
nia, with  3  water-wheels,  and  6  pair  of  stones. 

If  the  wheat  comes  by  water  to  the  mill  in  the 
ship  Z,  it  is  measured  and  poured  into  the  hopper 
A,  and  thence  conveyed  into  the  elevator  at  B, 
which  elevates  it,  and  drops  it  into  the  conveyer 
C  D,  which  conveys  it  along  under  the  joists  of 
the  second  floor,  and  drops  it  into  the  hopper  gar- 
ner at  D,  out  of  w^hich  it  is  conveyed  into  the  main 
wheat  elevator  at  E,  which  carries  it  up  into  the 
peak  of  the  roof,  and  delivers  it  into  the  rolling- 
screen  at  F,  which  (in  this  plan)  is  above  the  col- 
lar beams,  out  of  which  it  falls  into  the  hopper  G, 
thence  into  the  short  elevator  at  H,  which  conveys 
it  up  into  the  fan  I,  from  whence  it  runs  down 
slanting  into  the  middle  of  the  long  conveyer  at  j, 
that  runs  towards  both  ends  of  the  mill,  and  con- 
veys the  grain,  as  cleaned,  into  any  garner  KKK 
KKK,  over  all  the  stones,  which  is  done  by  shift- 
ing a  board  under  the  fan  to  guide  the  grain  to 
either  side  of  the  cog-wheel  j,  and  although  each 
of  these  garners  should  contain  2000  bushels  of 
wheat,  over  each  pair  of  stones,  12000  bushels  in 
6  garners,  yet  nearly  all  may  be  ground  out  with- 
out handling  it,  and  feed  the  stones  more  even  and 
regular  than  it  is  possible  to  do  in  the  old  way. 
As  it  is  ground  by  the  several  pairs  of  stones,  the 
meal  falls  into  th'^  meal  conveyer  at  M  M  M,  and 
is  conveyed  into  the  common  meal  elevator  at  N, 
which  raises  it  to  O,  from  thence  runs  down  the 
hopper-boy  at  P,  which  spreads  and  cools  it  over 


TO   THE  READER.  297 

a  circle  of  10  or  15  feet  diameter,  and  (if  thought 
best)  will  raise  over  it,  and  form  a  heap  two  or 
three  feet  high,  perhaps  tliirty  barrels  of  flour  or 
more  at  a  time,  which  may  be  bolted  down  at 
pleasuie.  When  it  is  bolting,  the  hopper-boy 
gathers  it  into  the  bolting  hoppers  at  Q,  and  at- 
tends them  more  regularly  than  is  ever  done  by 
hand.  As  it  is  bolted,  the  conveyer  R,  in  the  bot- 
tom of  the  superfine  chest,  conveys  the  superfine 
flour  to  a  hole  through  the  floor  at  S,  into  the 
packing  chest,  which  mixes  it  completely.  Out 
of  the  packing  chest  it  is  filled  into  the  barrel  at  T, 
weighed  in  the  scale  U,  packed  at  W  by  water, 
headed  at  X,  and  rolled  to  the  door  Y,  then  low- 
ered down  by  a  rope  and  windlas  into  the  ship 
again  at  Z. 

If  the  wheat  comes  to  the  mill  by  land,  in  the 
wagon  7,  it  is  emptied  from  the  bags  into  a  spout 
that  is  in  the  wall,  and  it  runs  in  the  scale  8,  which 
is  large  enough  to  hold  a  wagon  load,  and  as  it  is 
weighed  it  is  (by  drawing  a  gate  at  bottom)  let  run 
into  the  garner  D,  out  of  which  it  is  conveyed 
into  the  elevator  at  E.  and  so  through  the  same 
process  as  before. 

As  much  of  the  tail  of  the  superfine  reels  37 
as  we  think  will  not  pass  inspection,  we  suffer  to 
pass  on  into  the  short  elevator,  (by  shutting  the 
gates  at  the  bottom  of  the  conveyer  next  the  ele- 
vator, and  opening  one  further  towards  the  other 
end.)     The  rubblings.  which  fall  at  the  tail  of  said 

reels,  is  also  hoisted  into  the  bolting  hoppers  of 

pp 


298  TO  THE  READER. 

the  sifting  reel  39,  which  is  covered  with  a  fine 
cloth,  to  take  out  all  the  fine  flour  dust,  which 
will  stick  to  the  hran,  in  warm  dannp  weather,  and 
all  that  passes  through  it  is  conveyed  hy  the  con- 
veyer 40,  into  the  elevator  41,  which  elevates  it 
go  high  tliat  it  will  run  fi-eely  into  the  hopper-boy 
at  O,  and  is  bolted  over  again  with  the  ground 
meal.  The  rubbhngs  that  fall  at  the  tail  of  the 
sifting  reel  39,  fall  into  the  hopper  of  the  mid- 
dlings' reel  42  ;  and  the  bran  falls  at  the  tail  into 
the  lower  story.  Thus  you  have  it  in  your  power 
either  by  day  or  night,  without  any  hand  labour 
except  to  shift  the  sliders,  or  some  such  trifle,  to 
make  your  flour  to  suit  the  standard  quahty  ;  and 
the  most  superfine  possible  made  out  of  the  grain, 
and  finished  complete  at  one  operation. 

These  improvements  are  a  curiosity  worthy  the 
notice  of  the  philosopher  and  statesman,  to  see 
with  what  harmony  the  whole  machinery  works 
in  all  their  different  operations. 

But  to  conclude,  agreeably  to  request  I  attempt 
to  show  the  method  of  making  and  putting  water 
on  the  several  kinds  of  water-wheels  commonly 
used,  with  their  dimensions,  ^c.  suited  to  falls  and 
heads  from  3  to  36  feet;  and  have  calculated  ta- 
bles for  gearing  them  to  mill-stones;  and  made 
draughts*  of  several  water-wheels  with  their  fore- 
bays  and  manner  of  putting  on  the  water,  ^c. 

THOMAS  ELLICOIT. 


*  All  my  drauEfhts  are  taken  from  a  scale  of  8  feet  to  an  inch,  except 
nl.  V.  which  is  4  feet  to  an  inch 


THE 


PRACTICAL  MILLWRIGHT 


ART.    1. 
OF  UNDERSHOT  MILLS. 

FIG.  1,  plate  XIII,  represents  an  undershot  wheel  18 
feet  diameter,  with  3  feet  total  head  and  fall.  It  should 
be  2  feet^ide  for  every  foot  the  mill-stones  are  in  dia- 
meter ;  tnat  is,  8  feet  between  the  shrouds  for  a  -^  feet, 
and  10  feet  wide  for  a  5  feet  stone.  It  should  have  three 
sets  of  arms  and  shrouds,  on  account  of  its  great  width. 
Its  shaft  should  be  at  least  26  inches  diameter.  It  re- 
qtSires  12  arms,  18  feet  long,  3|  inches  thick,  by  9 
wide;  and  S4  shrouds,  7|  feet  long,  10  inches  deep,  by 
3  thick,  and  32  floats  15  inches  wide.  Note,  it  may  be 
geared  the  same  as  an  overshot  wheel,  of  equal  diame- 
ter. Fig.  2  represents  the  forebay,  with  its  sills,  posts, 
sluice  and  fall :  I  have  in  this  case  allowed  1  foot  fall 
and  2  feet  head.  * 

Fig.  3  represents  an  undershot  wheel,  18  feet  diame- 
ter, with  7  ^eet  head  and  fall.  It  should  be  as  wide  be- 
tween the  shrouds  as  the  stone  is  in  diameter.  Its  shaft 
should  be  2  feet  diameter.  Requires  8  arms  18  feet 
long,  3|  of  an  inch  thick,  by  9  wide.  And  16  shrouds, 
7i  feet  long,  10  inches  deep,  by  3  thick.  Note,  it  may 
be  geared  the  same  as  an  overshot  wheel  13  feet  diame- 
ter, because  their  revolutions  per  minute  will  be  nearly 
equal. 

Fig.  4  represents  the  forebay,  sluice,  and  fall,  the  head 
and  fall  about  equal. 


300  OF  UNDERSHOT  MILLS. 

Fig.  5  represents  an  undershot  wheel,  12  feet  diame- 
ter, with  15  feet  total  head  and  fall.  It  should  be  6 
inches  wide  for  every  foot  the  stone  is  in  diameter.  Its 
shaft  30  inches  diameter.  Requires  6  arms  12  feet  long, 
3  by  8  inches;  and  IS  shrouds,  6|  feet  long,  2{  inches 
thick,  and  8  deep.  It  suits  well  to  be  geared  to  a  5 
feet  stone  with  single  gears,  60  cogs  in  the  cog-wheel, 
and  16  rounds  in  the  trundle;  to  a  4|  feet  stone,  with 
62  cogs  and  15  rounds ;  and,  to  a  4  feet  stone,  with  64 
cogs  and  14  rounds.  These  gears  will  do  well  till  the 
fall  is  reduced  to  12  feet,  only  the  wheel  must  be  less  as 
the  falls  are  less,  so  as  to  make  the  same  number  of  re- 
volutions in  a  minute;  but  this  wheel  requires  more 
water  than  a  breast-mill,  with  the  same  fall. 

Fig.  6  is  the  forebay,  gate,  shute  and  fall.  Forebays 
should  be  wide  proportionable  to  the  quantity  of  water 
they  are  to  convey  to  the  wheels;  and  should  stand  8  or 
10  feet  in  the  bank,  and  be  firmly  joined,  to  prevent  the 
water  from  breaking  through;  which  it  will  c<^|ainly  d9, 
unless  thev  be  well  secured. 


,  ART.   2. 

DIRECTIONS  FOR  MAKING  FOREBAYS. 

The  best  way  that  I  know  for  making  these  kind  of 
forebays,  is  shown  in  plate  XVII,  fig.  7.  Make  a  number 
of  solid  frames,  consisting  of  a  sill,  two  posts,  and  a  cap 
each;  set  them  cross-wise,  (afB.shown  in  the  figure)  2| 
or  3  feet  apart;  to  these  the  plank  are  to  be  spiked,  for 
there  should  be  no  sills  lengthwise,  as  the  water  is  apt  to 
find  its  way  along  them.  The  frame  at  the  head  next 
the  water,  and  one  6  or  SlTeet  downwards  in  the  bank, 
should  extend  <t  or  5  feet  6n  each  side  of  the  forebay  in 
the  bank;  and  be  planked  in  front  to  prevent  the  water 
and  vermin  from  working  round.  Both  of  the  sills  of 
these  long  frames  should  be  well  secured,  by  driving 
down  plank  edge  to  edge,  like  piles,  -along  the  upper 
side,  from  end  to  end. 

The  sills  being  settled  on  good  foundations,  the  earth 


OF  UNDERSHOT  MILLS,  301 

or  gravel  must  be  rammed  well  on  all  sides,  full  to  the 
top  of  the  sills.  Then  lay  the  bottom  with  good  sound 
plank,  well  jointed  and  spiked  to  the  sills.  Lay  your 
shute,  extending  the  upper  end  a  little  above  the  point 
of  the  gate  when  full  drawn,  to  guide  the  water  in  a  right 
direction  to  the  wheel.  Plank  the  head  to  its  proper 
height,  minding  to  leave  a  suitable  shiice,  to  guide  the 
water  smoothly  down.  Fix  the  gate  in  an  upright  posi- 
tion— hang  the  wheel  and  finish  it  off  ready  for  letting  on 
the  water. 

A  rack  must  be  made  to  keep  oif  the  floating  trash  that 
would  break  the  floats  and  buckets  of  undershot,  breast, 
and  pitch-back  wheels,  and  injure  the  gates.  See  it  at 
the  head  of  forebay,  fig.  7,  plate  XVIL  This  is  done  by 
setting  a  frame  3  feet  in  front  of  the  forebaj^,  and  laying  a 
sill  2  feet  in  front  of  it,  for  the  bottom  of  the  rack ;  in  it 
the  staves  are  put,  made  of  laths,  set  edgewise  with  the 
stream,  2  inches  apart,  their  upper  ends  nailed  to  the  cap 
of  the  last  frame,  which  causes  them  to  lean  down  stream. 
The  bottom  of  the  race  must  be  planked  between  the 
forebay  and  rack,  to  prevent  the  w^ter  from  making  a 
hole  by  tumbling  through  the  rack  when  choked;  and 
the  side^  be  planked  outside  the  posts  to  keep  up  the 
banks.  This  rack  must  be  dotible  as  long  as  the  forebay 
is  wide,  or  els»  the  Xvater  will  not  come  fast  enough 
through  it  to  keep  the  head  up ;  for  the  head  is  the  spring 
of  motion  of  an  undershot  mill. 


ART.    3. 

jof  the  principle  of  undershot  mills. 

They  difler  from  all  others  in  principle,  because  the 
water  loses  all  its  force  by  the  first  stroke  against  the 
floats;  and  the  time  this  force  is  spending,  is  in  propor- 
tion to  the  difference  of  the  velocities  of  the  wheel  and 
water,  and  the  distance  of  the  floats.  Other  mills  have 
the  weight  of  the  water  after  the  force  of  the  head  is 
spent,  and  will  continue  to  move ;  but  an  undershot  will 
stop  as  soon  as  the  head  is  spent,  as  they  depend  not  on 


S02  OF  UNDERSHOT  MILLS. 

the  weight.  They  should  be  geared  so,  that  when  the 
stone  goes  with  a  proper  motion,  they  will  not  run  too 
fast  with  the  water,  so  as  not  to  receive  its  force ;  nor  too 
slow,  so  as  to  lose  its  power  by  rebounding  and  dashing 
over  the  buckets.  This  matter  requires  very  close  at- 
tention, and  has  puzzled  our  mechanical  philosophers  to 
find  it  out  by  theory.  They  give  us  for  a  rule,  that  the 
wheel  must  move  just  1-3  the  velocity  of  the  water:  per- 
haps this  may  suit  where  the  head  is  not  much  higher 
than  the  float- boards,  but  I  am  fully  convinced  it  will  not 
suit  high  heads. 

Experiments  for  determining  the  proper  Motion  for  Un^ 
dershot  Wheels. 

I  drew  a  full  sluice  of  water  on  an  undershot  wheel 
with  15  feet  head  and  fall,  and  counted  its  revolutions 
per  minute ;  then  geared  it  to  a  mill-stone,  set  it  to  work 
properly,  and  again  counted  its  revolutions,  and  the  differ- 
ence was  not  more  than  one-fourth  slower.  I  believe, 
that  if  I  had  checked  the  motion  of  the  wheel  to  be 
equal  1-3  the  motion  of  the  water,  that  the  water  would 
have  rebounded  and  flew  up  to  the  shaft.  Hence  I 
conclude,  that  the  motion  of  the  water  must  not  be 
checked  by  the  wheel  more  than  1-3,  nor  less  than  1-4; 
else  it  will  lose  in  power;  for  although  the  wheel  will 
carry  a  greater  load  with  the  slow,  than  swift  motion,  yet 
it  will  not  produce  so  great  effect,  its  motion  being  too 
slow.  And  again,  if  the  motion  be  too  swift,  the  load 
or  resistance  it  will  overcome  will  be  so  much  less,  that 
its  effect  will  be  lessened  also.  I  conclude,  that  about 
2-3  the  velocity  of  the  water  is  the  proper  motion  for 
undershot  wheels,  the  water  will  then  spend  all  its  force 
in  the  distance  of  two  float-boards ;  notwithstanding  the 
learned  authors  have  asserted  it  to  be  but  1-3.  To 
confute  them,  suppose  tlie  floats  12  inches,  and  the  co- 
lumn of  water  striking  them,  8  inches  deep;  then,  if 
2-3  of  the  motion  of  this  column  be  checked,  it  must 
instantly  become  24  inches  deep,  and  rebound  against 
the  backs  of  the  floats,  and  the  wheel  would  be  wal- 
lowing in  this  dead  water;  whereas,  when  1-3  of  its 
motion  is  checked,  it  becomes  only  \.%  inches  deep,  and 
runs  off"  from  the  wheel  smooth  and  livelv. 


OF  UNDERSHOT  WHEELS. 


303 


Directions  for  gearing  Undershot  Wheels^  18  feet  diame- 
ter, where  the  head  is  above  3  and  under  8  feet,  ivith 
double  gears  ;  counting  the  head  from  the  point  where 
the  water  strikes  the  floats. 

1.  For  3  feet  head  and  18  feet  wheel,  see  18  feet  wheel 
in  the  overshot  table. 

2.  For  3  feet  8  inches  head,  see  17  feet  wheel  in  said 
table. 

3.  For  4  feet  4  inches  head,  see  16  feet  wheel  in  do. 

4.  For  5  feet  head,  see  15  feet  wheel  in  do. 

5.  For  5  feet  8  inches  head,  see  l^  feet  wheel  in  do. 

6.  For  6  feet  4  inches  head,  see  13  feet  wheel  in  do. 

7.  For  7  feet  head,  see  12  feet  wheel  in  do. 

jAe  revolutions  of  the  wheels  will  be  nearly  equal  -; 
th#cfore  the  gears  may  be  the  same. 

The  following  table  is  calculated  to  suit  for  any  sized 
stone,  from  4  to  6  feet  diameter ;  different  sized  water- 
wheels  from  12  to  18  feet  diameter,  and  different  heads 
from  8  to  20  feet  above  the  point  it  strikes  the  floats. 
And  to  make  5  feet  stones  revolve  88  times ;  4  feet  6 
inch  stones  97  times ;  and  4  feet  stones  106  times  in  a 
minute,  when  the  water-wheel  moves  2-3  the  velocity  of 
the  striking  water. 

MILL-WRIGHT'S  TABLE  FOR  UNDERSHOT  MILLS— SINGLE 
GEARED. 


m 

Velocit 
tcrpe 
feet. 

Velocit 
ter-wl 
nnte  i 

llevolu 
water- 

^  z 

^  3 

■z 

■  ~  ft 

llevolu 
mill-s 
of      t 
wheel 

..  9. 

3  3 
n  n 

n   o 

i  " 

-  V; 

=  o^ 

n  :-  C. 

"w  *"* 

7^    '' 

O  "5 

en  ^  r—  *-• 

"  n 

->    -n 

S-'' 

3  ^ 

-^  1  o 

■  ^  o 

7i   3 

-5  - 

;,  c_ 

o_ 

■    n  °  o 

3  '' 

5'  ~ 

£.2- 

— '  ^ 

^■3  c; 

ft 

3  ^ 

~  c. 

^   -■ 

o=s 

-^"' 

'^  s 

—  c 

ft  O 

=  5 

^  o*  o 

ft  "^ 

re  — 

r-  <^ 

•■:  '^ 

-^ 

3  -^. 

•^  Ti 

P  -5  -*5 

5  o 

-■t 

If. 

•a  - 

it;  ~ 
-5  a 

?  a 

~  CB 

be 

ft  Oi 

7  n  n 

5- 

n 

8 

12 

1360 

9U6 

24 

88 

56 

15 

3  3-4 

5 

9 

13 

1448 

965 

23  1-2 

88 

58 

15 

37-8 

5 

10 

14 

1521 

1014 

23  1-7 

88 

58 

15 

3  6-7 

5 

11 

15 

1595 

1061 

22  3-4 

88 

58 

15 

334 

5 

12 

16 

1666 

1111 

22  1.4 

88 

58 

15 

3  7-8 

5 

13 

16 

1735 

1157 

231-7 

88 

60 

16 

3  3.4 

5 

14 

16 

18U0 

1200 

24 

88 

59 

16 

323 

5 

15 

16 

1863 

1242 

24  4-5 

88 

60 

17 

31-2 

5 

16 

16 

1924 

1283 

25  2-3 

88 

59 

17 

3  3-8 

5 

17 

17 

1983 

1322 

25 

88 

62 

17 

3  3-4 

5 

18 

17 

2041 

1361 

25  2-3 

88 

62 

17 

33  8 

5 

19 

18 

2097 

1398 

25 

88 

62 

17 

3  3-4 

5 

20 

18 

2H2 

1435 

25  1-2 

88 

60 

17 

o  .->  o 

5 

1 

2 

o 

4 

5 

6 

7 

8  1  9 

10 

504  OF  BREAST-WHEELS. 

Note  that  there  is  nearly  60  cogs  in  the  cog-wheel,  in 
the  foregoing  table,  and  60  inches  is  the  diameter  of  a  5 
feet  stone ;  therefore,  it  will  do  without  sensible  error,  to 
put  1  cog  more  in  the  wheel  for  every  inch  that  the  stone 
is  less  than  60  inches  diameter,  down  to  4  feet;  the  ti'un- 
dle  head  and  water-wheel  the  same. 

And  for  every  3  inches  that  the  stone  is  larger  than 
60  inches  in  diameter,  put  1  round  more  in  the  trundle, 
and  the  motion  of  the  stone  will  be  nearly  right  up  to  6 
feet  diameter. 


ART.    4. 

OFBREAST-WHEELS,  ^( 

Breast  Vvheels  differ  but  little  in  their  structure  or  mo- 
tion from  overshots,  excepting  only,  the  water  passes 
under  instead  of  over  them,  and  they  must  be  wider  in 
proportion  as  their  fall  is  less. 

Fig.  1,  plate  XIV,  represents  a  low^  breast  with  8  feet 
head  and  fall.  It  should  be  9  inches  wide  for  every  foot 
of  the  diameter  of  the  stone.  Such  wheels  are  generally 
18  feet  diameter;  the  number  and  dimensions  of  their  parts 
being  as  follows  :  8  arms  18  feet  long,  3  1-4  by  9  inches; 
16  shrouds  8  feet  long,  2  1-2  by  9  inches ;  56  buckets  ; 
and  shaft,  2  feet  diameter. 

Fig.  2.  shows  the  forebay,  water-gate,  and  fall,  and 
manner  of  striking  on  the  water. 

Fig.  3.  is  a  middling  breast-wheel  18  feet  diameter, 
with  12  feet  head  and  fall.  It  should  be  8  inches  wide 
for  every  foot  the  stone  is  in  diameter. 

Fig.  4.  shov.  s  the  forebay,  gate  and  fall,  and  manner  of 
striking  on  the  water. 

Fig.  5.  and  6.  is  a  high  breast-wheel,  16  feet  diameter, 
with  3  feet  head  in  the  forebay,  and  10  feet  fall.  It 
should  be  7  inches  wide  for  every  foot  the  stone  is  in 
diameter.  The  number  and  dimensions  of  its  parts  are, 
6  arms  16  feet  long,  3  1-4  by  9  inches  ;  12  shrouds  8 
feet  6  inches  long,  2|  by  8  or  9  inches  deep,  and  48 
buckets. 


QF  PITCH-BACK  WHEELS,  &c.  305 


ART.    5. 

OF  PITCH-BACK  WHEELS; 

Pitch  back  wheels  are  constructed  exactly  similar  to 
breast- wheels,  only  the  water  is  struck  on  them  higher. 
Fig.  1,  plate  XV,  is  a  wheel  18  feet  diameter,  with  3  feet 
head  in  the  penstock,  and  16  feet  fall  below  it.  It  should 
be  6  inches  wide  for  every  foot  of  the  diameter  of  the 
stone. 

Fig.  2  shows  the  trunk,  penstock,  gate,  and  fall,  the 
gate  sliding  on  the  bottom  of  the  penstock,  and  drawn  by 
the  lever  A,  turning  on  a  roller.  This  wheel  is  much 
recommended  by  some  mechanical  philosophers,  for  the 
saj^g  of  water ;  but  I  do  not  join  them  in  opinion,  but 
think  that  an  overshot  with  an  equal  head  and  fall,  is 
fully  equal  in  power;  besides  the  saving  of  the  expense  of 
so  high  a  wheel  and  fall,  that  are  difficult  to  be  kept  in 
order. 


ART.    6. 

OF  OVERSHOT  WHEELS. 

Overshot  wheels  receive  their  water  on  tlie  top,  being- 
moved  by  its  weight ;  and  are  much  to  be  recommended 
where  there  is  fall  enough  for  them.  Fig.  3  represents 
one  18  feet  diameter,  which  should  be  about  6  inches 
wide  for  every  foot  the  stone  is  in  diameter.  It  should 
hang  8  or  9  inches  clear  of  the  tail  water,  because  they 
draw  it  under  them.  The  head  in  the  penstock  should 
be  generally  about  3  feet,  which  will  spout  the  water 
about  1-3  faster  than  the  wheel  moves.  Let  the  shute 
have  about  3  inches  fall,  and  direct  the  water  into  the 
wheel  at  the  centre  of  its  top. 

I  have  calculated  a  table  for  gearing  overshot  wheels, 
which  will  equally  well  suit  any  of  the  others  of  equal 
diameter,  that  have  equal  heads  above  the  point  where 
the  water  strikes  the  wheel. 


a06  OF  OVERSHOT  WHEELS. 

Dimensions  of  this  wheel,  8  arms  18  feet  long,  3  by  9 
inches  ;  16  shrouds  7  feet  9  inches  long,  2|  by  7,  or  S 
inches  ;  56  buckets,  and  shaft,  24?  inches  diameter. 

Fig.  4  represents  the  penstock  and  trunk,  &c.  the 
water  being  let  on  the  v\  heel  by  drawing  the  gate  G. 

Fig.  1  and  2  plate  XVI,  represents  a  low  overshot  12 
feet  diameter,  which  should  be  in  width  equal  to  the  dia- 
meter of  the  stone.  Its  parts  and  dimensions  are,  6  arms 
12  feet  long,  3f  by  9  inches ;  12  shrouds  6|  feet  long, 
2 1  by  8  inches ;  shaft  22  inches  diameter,  and  30 
buckets. 

Fig.  3  represents  a  very  high  overshot  30  feet  diameter, 
which  should  be  3|  inches  wide  for  every  foot  of  the 
diameter  of  the  stone.  Its  parts  and  dimensions  are,  6 
main  arms,  30  feet  long,  3|  inches  thick,  10  inches  ^jde 
at  the  shaft,  and  6  at  the  end;  12  short  arms  14  wet 
long,  of  equal  dimensions ;  which  are  framed  into  the 
main  arms  near  the  shaft,  as  in  the  figure ;  for  if  they 
were  all  put  through  the  shaft,  they  would  make  it  too 
weak.  The  shaft  should  be  27  inches  diameter,  the 
wheel  being  very  heavy  and  bearing  a  great  load.  Such 
high  wheels  require  but  little  water. 


ART.    7. 
OF  THE  MOTION  OF  OVERSHOT  WHEELS. 

After  trying  many  experiments,  I  concluded  that  the 
circumiference  of  overshot  wheels  geared  to  mill-stones, 
grinding  to  the  best  advantage,  should  move  530  feet  in 
a  minute  ;  and  that  of  the  stones  1375  feet  in  the  same 
time  ;  that  is,  ivhile  the  wheel  moves  12,  the  stone  moves 
30  inches,  in  the  proportion  of  2  to  5. 

Then,  to  find  how  often  the  wheel  we  propose  to  make 
w^ill  revolve  in  a  minute,  take  the  following  steps  :  1st, 
Find  the  circumference  of  the  wheel  by  multiplying  the 
diameter  by  32,  and  dividing  by  7,  thus  : 


OF  GEARING. 


sor 


Suppose  the  diameter  to  be  16  feet,"1 
then  16  multiplied  by  22,  produces  I 
332;  which,  divided  by  7,  quotes  [ 
50  2-7  for  the  circumference.  J 

By  which  we  divide  550,  the  distance^ 
the  wheel  moves  in  a  minute,  and  it  j 
quotes   11,  for  the  revolutions  of  the  > 
wheel  per  minute,  casting  off  the  frac-  j 
tion  2-7,  it  being  small.  J 

To  find  the  revolutions  of  the  stone  ^ 
per  minute,  4?  feet  6  inches  (or  54  I 
inches)  diameter,  multiply  51  inches  I 
by^,  and  divide  by  7,  and  it  quotes  ' 
16T5-7  (say  170)  inches,  the  circum- 
ference of  the  stone. 

By  which  divide  1375  feet,  or  16500 
inches,  the  distance  the    skirt  of  the 
stone  should  move   in  a  minute,  and  . 
it   quotes    97;    the    revolutions    of    a  [ 
stone  per   minute,    4  1-S  feet  diame 
ter. 

To  find  how  often  the  stone  revolves"] 
for  once  of  the  water  wheel,  divide  97, 
the  revolutions  of  the  stone,  by  11,  the  > 
revolutions  of  the  wheel,  and  it  quotes  | 
8  9-il,  (say  9  times.)  J 


16 

22 

32 

32 

7)352 
50  2T 


5(0)5510 
11  times, 


54 

22 

108 

108 

7)1188 

16y  5T 


17lO)1650iO(9/ 
153 
120 
119 

1 


11)97(89-11 
88 


ART.    8. 
OP  GEARING. 


Now  if  the  mill  was  to  be  single  geared,  99  cogs  and 
11  rounds,  would  give  the  stone  the  right  motion,  but 
the  cog-wheel  would  be  too  large,  and  trundle  too  small, 
therefore  it  must  be  double  geared. 


308 


OF  GEARING. 


8441,  not  quite 


25 
15 

125 

25 

375 

66 

43 

528 

264 


375)3168(8168-375 
3000 
168 


Suppose  we  choose  66  cogs  in  the 
big  cog-wheel  and  48  in  the  httle  one, 
and  25  rounds  in  the  wallower,  and  15 
in  the  trundle. 

Then,  to  find  the  revolutions  of  the 
stone  for  one  of  the  \Aater- wheel,  mul-  y 
tiply  the  cog-wheels  together,  and  the 
wallower  and  trundle  together,  and 
divide  one  product  by  the  other,  and  it 
will  quote  the  answer, 
8 1  revolutions  instead  of  9 

Therefore  we  must  make  another  proposition — Consi- 
dering which  of  the  wheels  we  had  best  alter,  and  wish- 
ing not  to  alter  the  big  cog-wheel  nor  trundle,  we  put 
one  round  less  in  the  wallower,  and  two  cogs  more  imthe 
little  cog-wheel,  and  multiplying  and  dividing  as  before, 
we  find  the  stone  vvill  turn  9  1-6  times  for  once  of  the 
water-wheel,  which  is  as  near  as  we  can  get.  The  mill 
now  stands  thus,  a  16  foot  overshot  wheel,  that  will  re- 
volve 11  times  in  a  minute,  geared  to  a  stone  4  l-2>  feet 
diameter;  the  big  cog-wheel  66  cogs,  4  12  inches  from 
centre  to  centre  of  the  cogs;  (which  we  call  the  pitch  of 
the  gear)  little  cog-wheel  50  cogs  4|  pitch;  wallower  2^ 
rounds,  4|  pitch,  and  trundle  15  rounds,  4^  inches 
pitch. 


ART.    9. 
RULES  FOR  FINDING  THE  DIAMETER  OF  THE  PITCH  CIRCLES. 


To  find  the  diameter  of  the  pitch  "| 
circle,  that  the  cogs  stand  in,  multiply  I 
the  number  of  cogs  by  the  pitch,  | 
which  gives  the  circumference;  which,  I 
multiplied  by  7,  and  divided  by  22,  f 
gives  the  diameter  in  inches;  which, 
divided  by  12,  reduces  it  to  feet  and 
inches  thus : 


66 

_4| 

264 

33 

297 

f 

22)2079(94^  in. 
198 

99 
88 
11 


RULES  FOR  FINDING  THE  DIAMETER,  &c.  309 

For  the  cos^-wheel  of  66  cogs,  4|  pitch,  we  find  to  be  7 

feet  10  1 1  -S3  inches,  the  diameter  of  the  pitch  circle ;  to 

which  I  add  8  inches,  for  the  outside  of  the  cogs,  makes  8 

feet  6|  inches,  the  diameter  from  out  to  out. 

By  the  same  rules  I  find  the  diameters  of  the  pitch 

circles  of  the  other  wheels,  to  be  as  follows,  viz. 

ft.  in. 

Little  coar- wheel  50  coffs,  40        t       ^n  m  oo 
.,^vr  &'2C        5       71  10-22  p.  cir. 

mches  pitch,  ^  z  i 

I  add  for  the  outside  of  the  circle,  7| 


Total  diameter  from  out  to  out  6  3 

Wallower  24  rounds  41  inches  7  o  n    o  >«  ^  <nr^ 

rftch,                                        S  2  113-4  4-22 

Acid  for  outsides,  0  3  18-22  do. 


Total  diameter  from  the  outsides,      3     3 

Trundle  head  15  rounds  4|  inch  7      .     8^  ^  22  d 

pitch,  3  "^    ' 

Add  for  outsides,  S|  19  32 

Total  diameter  for  the  outsides,         111 

Thus  we  have  completed  the  calculations  for  one  mill, 
with  a  16  feet  overshot  water-wheel,  and  stones  41  feet 
diameter.  By  the  same  rules  we  may  calculate  for  wheels 
of  all  sizes  from  12  to  30  feet,  and  stones  from  4  to  6 
feet  diameter,  and  may  form  tables  that  may  be  of  great 
use  to  many,  even  to  master- workmen  that  understand 
©alculating  well  in  despatching  of  business,  in  laying  out 
work  for  their  apprentices  and  other  hands,  getting  out 
timber,  &c.  but  more  especially  to  those  who  are  not 
learned  in  arithmetic  sufficient  to  calculate,  I  beinar  from 
long  experience  highly  sensible  of  the  need  of  such  a 
table,  have  therefore  undertaken  the  arduous  task. 


310         EXPLANATION  OF  THE  TABLES. 


MILL- WRIGHTS'  TABLES, 

Calculated  to  suit  overshot  water-wheels  with  suitable 
heads  above  them,  of  all  sizes  from  IS  to  30  feet  diame- 
ter, the  velocity  of  their  circumferences  being  about  550 
feet  per  minute,  showing  the  number  of  cogs  and  rounds 
in  all  the  wheels,  double  gear,  to  give  the  circumference 
of  the  stone  a  velocity  of  1375  feet  per  minute,  also  the 
diameter  of  their  pitch  circles,  the  diameter  of  the  out- 
sides,  and  revolutions  of  the  water-wheel  and  stones  per 
minute. 

For  particulars  see  what  is  written  over  the  head  of 
each  table.  Table  I,  is  to  suit  a  4  feet  stone,  table  II,  a 
41,  table  III,  a  5  feet,  and  table  IV,  a  5|  feet  stone. 

N.  B.  If  the  stones  should  be  an  inch  or  two  biggeiior 
less  than  those  above  described,  make  use  of  the  table 
that  comes  nearest  to  it,  and  likewise  for  the  water-wheels. 
For  further  particulars  see  draughting  mills. 

Use  of  the  folio-wing  Tables. 

Having  levelled  your  mill-seat  and  found  the  total  fall, 
after  making  due  allowances  for  the  fall  in  the  races,  and 
below  the  wheel,  suppose  there  is  SI  feet  9  inches,  and 
the  mill- stones  are  4  feet  diameter,  then  look  in  table  I, 
(which  is  for  4  feet  stones)  column  3,  for  the  fall  that  is 
nearest  yours,  and  you  find  it  in  the  7th  example  :  and 
against  it  in  column  8,  is  the  head  proper  to  be  above  the 
wheel  3  feet,  in  column  4  is  18  feet,  for  the  diameter  of 
the  wheel,  &c.  for  all  the  proportions  of  the  gears  to  make 
a  steady  moving  mill,  the  stones  to  revolve  106  times  in 
a  minute.* 

•  The  following  tables  are  calculated  to  give  the  stones  the  revolution 
per  minute  mentioned  in  them,  as  near  as  any  suitable  numberof  cogs  and 
rounds  would  permit,  which  motion  1  find  is  8  or  10  revolutions  per  minute 
slower  than  proposed  by  Evans  in  his  table;— his  motion  may  do  best  in 
cases  where  'here  is  plenty  of  power  and  steady  work  on  one  kind  of  gram ; 
but  in  country  mills,  where  they  are  continually  changing  from  one  kind 
to  another,  and  often  starting  and  stopping,  I  presume  a  slow  motion  will 
work  most  regular.  His  table  bemg  calculated  for  only  one  size  of  mill- 
stones, and  mine  for  four,  if  any  choose  his  motion,  look  for  the  width  of 
the  water-wheel,  number  of  cogs,  and  rounds  and  size  of  the  wheels  to 
suit  them,  in  the  next  example  following,  keeping  to  my  table  in  other  re- 
spects, and  you  will  have  his  motion  nearly- 


TABLES,  &c. 


311 


TABLE  I.  For  Overshot  Mills  with  Stones  4  feet  Diameter,  to  revolve  106 
times  in  a  minute,  pitch  of  the  gear  of  great  cog  wheel  and  wallowers 
4i  inches,  and  of  lesser  cog  wheel  and  trundle  4i  inches. 


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TABLES,  &c. 


TABLE  II.  For  Overshot  Mills  with  Stones  4  feet  6  inches  Diameter,  to 
revolve  99  times  in  a  minute,  pitch  of  the  gems  4A  inches  and  4i  in- 
ches. 


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5,10,33 

9.3 
6,6 

26 
15 

3,125    3.4.25 
i,833    1.115 

l0  5 

7 

21,9 

3,0 

18 

'.^  ^^^ 

8,725 
5.10.33 

9.3 
6,6 

25 
14 

2,11.75  3,3 
1.7         1,11.5 

10 

8 

22.10 

3,1 

19 

'■*  ^i 

8,7.25 
5,10.33 

9,3 
6,6 

24 
14 

2.10  33  3,2  5 
1,7         1.115 

9.5 

2,3      ^52 

8,11.33 

9.7.33 

24 

2.10.33  3,2.5        „    1 

9 

23,11 

3,2 

20 

5,10  33 

6,6 

14 

1,7 

1,11.5       '' 

10 

25,1 

3,4 

21 

,.  Ill 

8,11.33 
5,1033 

9,7.33 
6.6 

23 
14 

2.9 
1,7    ^^ 

.3,0        '      s 
1,115    ^-^^ 

11 

26,3 

3,6 

22 

^A  III 

9,3.5 
5,10.33 

9,11.5 
6,6 

24 
14 

2,10.333,2.5         n- 

1,7    ;i,ii.5  ^-^^ 

12 

27,5 

3.8 

23 

.,0     {g 

9,3.5 
5,10.33 

9,11.5 
6,6 

23 
14 

2,9 

1,7 

3,0             ocr 

1,11.5    "-^ 

13 

28,7 

3,10 

24 

-."  v^ 

9,3.5 
6.1 

9,11.5 
6,8.5 

2- 
14 

2,9 
1,7 

3,0            a 
1,11.5       ** 

14 

29,9 

4,0 

25 

MO  ffl 

9.8 
6,1 

10,4 
6,8.5 

23 
14 

2,y 
1,7 

^•^        7  75 
1,115    '^^ 

15 

30,11 

4,2 

26 

'.^  f.^J 

9,8 
6,3-25 

10,4 
6,11.25 

2;i 
14 

2,9 

1.7 

3.U        7, 
1,11.5    ^^ 

16 

32,1 

4.4 

27 

'.3    Ce 

10.0  25 
6,3  25 

10.825 
6.11.25 

2,-"> 
14 

2,9 
1,7 

1,115   ^'^ 

17 

33,3 

4,6 

28 

'.«    {^^ 

10.0-25 
6,625 

10.8  25 
7.125 

23 
14 

2.9 
1,7 

3'^         6  66 
1,115    °-^^ 

■■=    {It 

10,025 

10,8.25 

.^  T 

2,9 

3,0         .^ 

18 

34.6 

4,9 

29 

6,3-25 

6,1125 

13 

I  5.25  1,825   ""    / 

>.^  ir^ 

10.0  75 

10.825 

22 

2,7.5    12,10  5    .,, J 

19 

35,9 

5,0 

30 

6,325 

6,11.25 

13    i.5  2  5:l.b25    -  "•' | 

TABLES,  &c. 


313 


TABLE  III.    Stones  5  feet  Diameter,  to  revolve  86  times  in  a  minute,  the 
pilch  of  the  gears  4^  and  4^  incheS' 


^ 

^ 

C 

^ 

& 

2: 

c 

5 

25 

O 

H 

^ 

Zii 

5; 

K 

3 

o 

T>    3 

3 

c 

<  3 

s 

< 
O 

z 

n 

3- 

in 

■»5 

o 

^2 

n 

-1 

n 

5    01 

D. 

•a  5 

p 

—     2- 

?  5 

0   c_ 

3   in 

—  o 

m 

2  o 

q  S. 

n 
-J   O 

si 

"»» 

T      ZT     - 

"  * 

"Z.    ^ 

o   .■ 

O    "^ 

ft  -»i 

f^    "^ 

c   * 

Bl     -»J 

a'o 

»  n  ? 

n 

0  E. 

1   re 

29     -^ 

^  ~ 

to 

=  8 

3     - 

5-H. 

S    CO 

s   "*• 

w 

•    n>  't 

ifc 

.^     IT 

-« 

?    T 

"^  « 

O  3R 

^  i 

M      *" 

3 

i*    3- 

3 
n 

CO 

3    ~ 
cr    ;^. 

O    O 

n    3 

3-  j: 

'5     t- 
O     - 

r"  f» 

r    -: 
n 

to 

rti   -! 

6: 

3 

o 
=?  2. 

n 

2 

o 

3    O 

C-  n' 

n 

3 

P    -i 
-»    re 

°  n 

^ 

s 

». 

2  (^ 
2,  w 

:?» 

n 
^ 

(0     ft 

3= 

s-  X 

O 

d 

^ 

(T 

U) 

d 

re 

ft 

. 

-■5 

a 

3 

S 

o 

-»5 

3 

e- 

5' 

oi 

2- 

ft    in. 

r  u 

r,e 

ft.WI. 

fi.  .n. 

r  Ml. 

It    in. 

ft.  til. 

1 

15.3 

2,6 

12 

*.»      |48 

7,6.12 
5,4.87 

8.2.12 
6.0.5 

26 
16 

3,1.25 
1,9  66 

3,4.25 
2.4.25 

13 

2 

16,4 

2,7 

13 

3.>0  J- 

7.10.5 
5,4.87 

8.6.5 
6,0  5 

26 
16 

3,125 
1,9  66 

3,4.25 
2,4.25 

12.5 

3 

17.5 

2,8 

14 

3.B     ft^ 

7,10.5 
5,4.87 

8.6.5 
6.0.5 

25 
15 

2,11.75 
1,8  33 

3,3 
1.11.33 

12 

4 

18,6 

2,9 

15 

^■^     ^^^ 

8,2  33 
5,4  87 

8,10  33 
6,0.5 

26 
15 

3,125 
1,8.33 

3,4.25 
1,11.33 

11.5 

5 

19,7 

2,10 

16 

-  A      ?69 
^'4      |48 

8,2  33 
5,4.87 

8,10.3o 
6,0  5 

25 
15 

2,11.75 
1,8.33 

3,3 
1.11.5 

11 

6 

20,8 

2.11 

17 

3.2      {f. 

8,233 
5,7.3 

8,10.33 
6,3 

25 
15 

2,11.75 

1,8.33 

3,3 
1.115 

105 

7 

21,9 

3.0 

18 

3.0      1^^ 

8.7.25 
5,10,33 

9.3 
6,6 

26 
15 

3,1.25 
1,833 

3,4.25 
1,11.33 

10 

8 

22,10 

3.1 

19 

07'^ 

8,7  25 

5,10.3.; 

9.3 
6.6 

25 
14 

2,11.75 
1,7 

3,3 
1,11.5 

9  66 

9 

23,11 

3,2 

20 

^■«  p.^ 

8.7.25 
5,1033 

9,3 
6,6 

24 
14 

2,1033 
1.7 

3'^^      9  25 
1,11.5   ^'^^ 

10 

25,1 

3,4 

21 

2<^  J^^ 

8,11  33 
5,10.33 

9.7.33 
6,6 

J4 
14 

2,10  333,2.5 
1.7        1,11.5 

8  87 

11 

26,3 

3,6 

22 

-  Vsi 

8,11.33 
5,10.33 

9,7.33 
6,6 

23 
14 

2.9 
1.7 

3,0 
1.11.5 

8.5 

12 

27,5 

3,8 

23 

^■^  m 

9,3.5 

5,10.33 

9,11.5 
6,6 

24 
14 

2.10.33 
1,7 

3.2.33 
1,11.5 

8.25 

13 

28,7 

3,10 

24 

^■^  III 

9,35 
5,10  33 

9.11.5 
6,6 

23 

14 

2.9 
1.7 

3,0 
1,11.5 

8 

14 

29,9 

4,0 

25 

^■=  m 

9,3  5 
6,1 

9,11.5 
6.8.5 

23 
14 

2,9 
1.7 

3,0 
1,115 

7.75 

15 

30  11 

4.2 

26 

2.0    ^?l 

9,8 
6,1 

10,4 
6,8  5 

23 
14 

2,9 
1.7 

3,0 
1,11.5 

75 

16 

32.1 

4,4 

27 

M.  c^ 

9.8 
6,3  25 

10,4 
6.1125 

23 
14 

2.9 
1.7 

3,0 
1.11.5 

6.33 

1 

17 

33,3 

4,6 

28 

'.'    Oa 

10,0  25 
6,3  25 

10,8  25 
6,1125 

23 
14 

2.9 
1.7 

3,0 
1,115 

6.66 

18 

34,6 

4.9 

29 

••'  {% 

10.0.25 
6,6.25 

10.8  25 
7.125 

23 
14 

2.9 
1.7 

?;?i.5  «^ 

19 

35.9 

5.0 

30 

•.<=  i^J 

10.0.25 
6.3  25 

10,8  25 
6.1125 

23 
13 

2,9 
1,5.25 

n.s  ^-^^ 

j^  r 


314, 


TABLES,  &c. 


TABLE  IV.  For  Overshot  Mills  with  Stones  5  feet  6  inches  Diameter,  to 
revolve  80  times  in  a  minute,  pitch  of  the  gears  4|  inches  and  4i  in 
cbes. 


o  o  2 

C 

C 

^ 

c 

f 

z 

9 

O 

H 
1^ 

?3 

.-5 

-^  -^  6- 

n 

'      3 

Q- 

S  ^ 

3 

o 

^  3 

p 

o_ 

? 

tfi 

n 

IT 

n 

© 

M     O 

p  ft 

'^  n 
p  -J 

3    CO 

n 

n 
1 
ce 

o  -> 

V  £■ 

3  1' 

o_ 

=  B'c 

ft*    as 

=  £. 

« 

CO   J3 

-J     01 

IT  o 

=  2, 

s-g. 

1    O 

s-i 

5-^ 

ft 
»4 

f^l 

O    CO 

-3 

O    V 

o  s 

3    3 

ce    -*s 
3  ^ 

a 

—  ■  n    -- 
-3    w    ^ 

2  7 

rr- 

F 

i^ 

O  vq 

—  3- 
1    " 

O 

=1    ^ 

3 

3  — 

p    6: 

t 

ill 

o  re 

re 
2. 

VI 

S 

=r  o 

2.    (D 

zr 
n 
n 

(0 

§0 

CO  n> 

U9 

o 

V!    c 

n 

n 

o  o 

o 
a 

f.  i. 

o 
3 

fe^-t. 

r.  I. 

3 

o 

d 
3 

3 

ft.  in. 

h 

f.    m. 

f.     1. 

f     1. 

1 

15,3 

2,6 

12 

4g     r60    7,6  75 
*'°      1  48'  5,8  75 

8,2.75 
6,4  25 

26 
16 

3,3.25 
1,11 

3,6-25 

2,2 

13 

2 

16,4 

2.7 

13 

,.     1  63i  7,1112 
*'*      1 48!  5,8  75 

8,7.12 

6,425 

26 
16 

3,3  25 
1,11 

3,6.25 
2,2 

125 

3 

ir,5 

28 

14 

*■=  JS 

8,3  75 
5,875 

8,1175 

6,4  25 

26 
16 

3,3.25 
1,11 

3,6.25 
2,2 

12 

4 

18,6 

2.9 

15 

^.»  U^ 

8.3.75 
5,8,75 

8,1175 
6,4  25 

26 
15 

3,3  25 
1.9  5 

3,6.25 
2.0.5 

11.5 

5 

i9.r 

2,10 

16 

o    1f^      ^69 

^.10   [48 

8,8  33 
5,8.75 

9,4.33 
6,4.25 

26 
15 

3  3  25 
1,9.5 

3,6.25 
2.0-5 

11 

6 

20,8 

2.11 

17 

-ft     1  69 

8,8  33 
5,8.75 

9,4.33 
6  4  25 

25 
1) 

3,175 
1,95 

3,4-75 
2,0.5 

10.5 

7 

21,9 

3,0 

18 

^.«  f?? 

8,8.33 
5,115 

9,4  33 
62  5 

25 
15 

3,1  75 
1,95 

3,4.75 
2,0.5 

9 

8 

22,10  3,1 

19 

^■*  Is 

9.0.75 
6,2.5 

9,8  75 
6,10 

26 
14 

3,325 
1,8 

3,625 
1,11 

9.66 

9 

23,11  3,2 

20 

^•^  f^2 

9,0.75 
6,2.5 

9,8.75 
6,10 

25 
14 

3  175 
1,8 

3,4-75 
1,11 

9  25 

10 

25,1   '3,4 

j 

21 

=.»  U^ 

9,0  75 
6,2.5 

9,8  75 
6,10 

24 
14 

3.0  75 
1,8 

3,3-75 
1,11 

8.12 

11 

26,3 

3,6 

22 

''in  r 

9,5.33 

10,1.33 

23 

3,075 

3375 

85 

^,iu    1  ^2 

6,2.5 

6,10 

14 

1,8 

1,11 

12 

27,5 

3,8 

23 

2>3  Ui 

9,5.33 

6.2.5 

10,1.33 
6,10 

23 
14 

2,10.75 
1,8 

3,1.75 
1,11 

825 

13 

28,7 

3,10 

24 

^>«  r^^ 

9,10.5 
6,2.5 

10,6 
6,10 

24 
14 

3,U.75 
1,8 

3,3.75 
1.11 

8 

14 

29,9 

4,0 

25 

2.^  Is 

9,10  5 
6,25 

10,6 
6,10 

23 
14 

2,10.75 
1,8 

3,1.75 
1.11 

7.75 

15 

30,11 

4.2 

26 

0  9    r78 

■''^     J  54 

9,10  5 
6,5.33 

10,6 
7,1 

23 
14 

2,10  75 
1,8 

3,175 
1,11 

7.5 

16 

32.1 

4,4 

27 

^0  r^ 

10,2.5 

10,10.5 

23 

2,10.75 

3,175 

6.75 

~'^     1 54 

6,5.33 

7,1 

14 

1.8 

1,11 

17 

33,3 

4,6 

28 

■."  j?J 

10,2  5 
6,8 

10,10  5 

7.:is 

23 
14 

2,10.75 
1,8 

3,1-75 
1,11 

6.66 

18 

34,6 

4,9 

29 

■.'»  Is 

10,7 
6,8 

11,3 
7,3.5 

23 
14 

2,1075 
1,8 

3,1,75 
1,11 

6.5 

19 

35,9 

5,0 

30 

■.^  f^J 

1U,7 
6,11 

113 

7,6.5 

23 
14 

2,10.75 
1,8 

3,1.75 
1,11 

6.25 

OF  CONSTRUCTim;  WHEELS.  315 

ART.    10. 

V)IRECtlONS  FOR  CONSTRUCTING  UNDERSHOT  WHEELS,  SUCH 
AS   FIG     1,  PLATE  XHI. 

1.  Dress  the  arms  straight  and  square  on  all  sides,  and 
find  the  centre  of  each  ;  divide  each  into  4-  equal  parts  on 
the  side  square  centre  scribe,  and  gauge  them  from  the 
upper  side  across  each  point,  on  both  sides,  6  inches  each 
way  from  the  centre. 

S.  Set  up  a  truckle  or  centre-post,  for  a  centre  to  frame 
the  wheel  on,  in  a  level  place  of  ground,  and  set  a  stake 
to  keep  up  each  end  of  the  arms  level  with  the  truckle, 
of  convenient  height  to  work  on. 

3.  Lay  the  first  arm  with  its  centre  on  the  centre  of  the 
truckle,  and  take  a  square  notch  out  of  the  upper  side  3-4 
of  its  depth,  wide  enough  to  receive  the  2d  arm. 

4.  Make  a  square  notch  in  the  lower  edge  of  the  2d 
arm,  1-4  of  its  depth,  and  lay  it  in  the  other,  and  they 
will  joint  standing  square  across  each  other. 

5.  Lay  the  3d  arm  just  equi-distant  between  the  others, 
and  scribe  the  lower  arms  by  the  side  of  the  upper,  and 
the  lower  edge  of  the  upper  by  the  sides  of  the  lower 
arms.  Then,  take  the  upper  arm  off"  and  strike  the 
square  scribes,  taking  out  the  lower  half  of  the  3d  arm, 
and  the  upper  half  of  the  lower  arms,  and  fit  and  lay  them 
together. 

6.  Lay  the  4th  arm  on  the  others,  and  scribe  as  direct- 
ed before ;  then  take  3-4  of  the  lower  edge  of  the  4?  h 
arm,  and  1-4  out  of  the  upper  edge  of  the  others,  and 
lay  them  together,  and  they  will  be  locked  together  in 
the  depth  of  one. 

7.  Make  a  sweep-staff  with  a  gimblet  hole  for  the 
centre  at  one  end,  which  must  be  set  by  a  gimblet  in  the 
centre  of  the  arms.  Measure  from  this  hole  half  the  di- 
ameter of  the  wheel,  making  a  hole  there,  and  another  the 
depth  of  the  *jhrouds  towards  the  centre,  making  each 
edge  of  this  sweep  at  the  end  next  the  shrouds,  straight 
towards  the  centre  hole,  to  scribe  the  ends  of  the  shrouds 
by. 

8.  Circle  both  edges  of  the  shrouds  by  the  sweep, 


316  OF  CONSTRUCTING  WHEELS. 

dress  them  to  width  and  thickness,  lay  out  the  laps  5 
inches  long,  set  a  gauge  to  a  little  more  than  1-3  their 
thickness,  gauge  all  their  ends  for  the  laps  from  the  out- 
sides,  cut  them  all  out  but  the  last,  that  it  may  be  made 
a  little  longer,  or  shorter,  as  may  suit  to  make  the  wheel 
the  right  diameter ;  sweep  a  circle  on  the  arms  to  lay  the 
shrouds  to,  while  fitting  them,  put  a  small  draw-pin  in  the 
middle  of  each  lap,  to  draw  the  joints  close,  strike  a  true 
circle  for  both  inside  and  outside  the  shrouds,  and  one 

1  1-2  inch  from  the  inside,  where  the  arms  are  to  be  let  in. 

9.  Divide  the  circle  into  8  equal  parts,  coming  as 
near  the  middle  of  each  shroud  as  possible ;  strike  a 
scribe  across  each  to  lay  out  the  notch  by,  that  is  to  be 
cut  by  1 1  inch  deep,  to  let  in  the  arm  at  the  bottom  of 
"where  it  is  to  be  forked  to  take  in  the  remainder  of  the 
shroud.  Strike  a  scribe  on  the  arms  with  the  same  sweep 
that  the  stroke  on  the  shrouds  for  the  notches  was  struck 
with. 

10.  Scribe  square  down  each  side  of  the  arms,  at  the 
bottom  of  where  they  are  to  be  forked ;  make  a  gauge 
to  fit  the  arms,  so  wide  as  just  to  take  in  the  shrouds,  and 
leave  1 1  inch  of  wood  outside  of  the  mortise ;  bore  1  or 

2  holes  through  each  end  of  the  arms  to  draw-pin  the 
shrouds  to  the  arms  when  hung;  mark  all  the  arms  and 
shrouds  to  their  places,  and  take  them  apart. 

11-  Fork  the  arms,  put  them  together  again,  and  put 
the  shrouds  into  the  arms;  drawbore  them,  but  not  too 
much,  which  would  be  worse  than  too  little  ;  take  the 
shrouds  apart  again,  turn  them  the  other  side  up,  and 
draw  the  joints  together  with  the  pins,  and  lay  out  the 
notches  for  4  floats  between  each  arm,  32  in  all,  large 
enough  for  admitting  keys  to  keep  them  fast,  but  allow- 
ing them  to  drive  in  when  any  thing  gets  under  the 
wheel.  The  ends  of  the  floats  must  be  dovetailed  a  little 
into  the  shrouds ;  when  one  side  is  framed,  frame  the 
other  to  fellow  it.  This  done,  the  wheel  is  ready  to  hang, 
but  remember  to  face  the  shrouds  between  the  arms  with 
inch  boards,  nailed  on  with  strong  nails,  to  keep  the 
wheel  firm  together. 


OF  CONSTRUCTING  WHEELS.  317 

ART.    11. 

DIRECTIONS  FOR  DRESSING  SHAFTS,  5tc. 

The  shaft  for  a  water-wheel  with  8  arms  should  be 
16  square,  or  16  sided,  about  2  feet  diameter,  the  tree 
to  make  it  being  2  feet  3  inches  at  the  top  end.  When 
cut  down  saw  it  off  square  at  each  end  and  roll  it  on 
level  skids,  and  if  it  be  not  straight,  lay  the  rounding 
side  down  and  view  it,  to  find  the  spot  for  the  centre  at 
each  end.  Set  the  big  compasses  to  half  its  diameter, 
and  sweep  a  circle  at  each  end,  plumb  a  line  across  each 
centre,  and  at  each  side  at  the  circle,  striking  chalk  lines 
over  the  plumb  lines  at  each  side  from  end  to  end,  and 
•dress  the  sides  plumb  to  these  lines ;  turn  it  down  on 
one  side,  setting  it  level ;  plumb,  line,  and  dress  off  the 
sides  to  a  4  square  ;  set  it  exactly  on  one  corner,  and 
plumb,  line,  and  dress  off  the  corner  to  8  square.  In  the 
same  manner  dress  it  to  16  square. 

To  cut  it  square  off  to  its  exact  length,  stick  a  peg  in 
the  centre  of  each  end,  take  a  long  square  (that  may  be 
made  of  boards)  lay  it  along  the  corner,  the  short  end 
against  the  end  of  the  peg,  mark  on  the  square  where 
the  shaft  is  to  be  cut,  and  mark  the  shaft  by  it  at  every 
corner  line,  from  mark  to  mark ;  then  cut  it  off  to  the 
lines,  and  it  will  be  truly  square. 


ART.  12. 

TO  LAY  OUT  THE  MORTISES  FOF  THE  ARMS. 

Find  the  centre  of  the  shaft  at  each  end,  and  strike  a 
circle,  plumb  a  line  through  the  centre  at  each  end  to  be 
in  the  middle  of  two  of  the  sides  ;  make  another  scribe 
square  across  it,  divide  the  distance  equally  between 
them,  so  as  to  divide  the  circle  into  8  equal  parts,  and 
strike  a  line  from  each  of  them,  from  end  to  end,  in  the 
middle  of  the  sides ;  measure  from  the  top  end  about 
3  feet,  and  mark  for  the  arm  of  the  water-wheel,  and 
the  width  of  the  wheel,  and  make  another  mark.     Take 


318  OF  CONSTRUCTING  WHEELS. 

a  straight  edge  10  feet  pole,  and  put  the  end  even  with 
the  end  of  the  shaft,  and  mark  on  it  even  with  the  marks 
on  the  shaft,  and  by  these  marks  measure  for  the  arm 
at  ever}-  corner,  marking  and  lining  all  the  way  round. 
Then  take  the  uppermost  arms  of  each  rim,  and  by  them 
lay  out  the  mortises,  about  half  an  inch  longer  than  they 
are  wide,  which  is  to  leave  key  room  ;  set  the  compasses 
a  little  more  than  half  the  thickness  of  the  arms,  and 
set  one  foot  in  the  centre  line  at  the  end  of  the  mortise, 
striking  a  scribe  each  way  for  to  lay  out  the  width  by  ; 
this  done,  lay  out  2  more  on  the  opposite  side,  to  com- 
plete the  mortises  through  the  shaft.  Lay  out  2  more 
square  across  the  first,  one  quarter  the  width  of  the  arm, 
longer  inward,  towards  the  middle  of  the  wheel.  Take 
notice  which  way  the  locks  of  the  arms  wind,  whether 
to  right  or  left,  and  lay  out  the  third  mortises  to  suit, 
else  it  will  be  a  chance  whether  they  suit  or  not :  these 
must  be  half  the  width  of  the  arms,  longer  inwards. 

The  4th  set  of  mortises  must  be  |  longer  inwards  than 
the  width  of  the  arms ;  the  mortises  should  be  made 
rather  hollowing  than  rounding,  that  the  arms  may  slip 
in  easily  and  stand  fair. 

If  there  be  three  (which  are  called  6)  arms  to  the  cog- 
wheel, but  1  of  them  can  be  put  through  the  sides  of  the 
shaft  fairly  ;  therefore,  to  lay  out  the  mortises,  divide  the 
end  of  the  shaft  anew,  into  but  6  equal  parts,  by  striking 
a  circle  on  each  end  ;  and  without  altering  the  compasses, 
step  from  one  of  the  old  lines,  six  steps  round  the  circle, 
and  from  these  points  strike  chalk  lines,  and  they  will  be 
the  middle  of  the  mortises,  which  may  be  laid  out  as 
before,  minding  which  way  the  arms  lock,  and  making 
2  of  the  mortises  1-3  longer  than  the  width  of  the  arm, 
extending  1  on  one  side,  and  the  other  on  the  other  side 
of  the  middle  arm. 

If  there  be  but  2  (called  4)  arms  in  the  cog-wheel, 
(which  will  do  where  the  number  of  cogs  do  not  exceed 
60)  they  will  pass  fairly  through  the  sides,  whether  the 
shaft  be  12  or  16  sided.  One  of  these  must  be  made 
one  half  longer  than  the  width  of  the  arms,  to  give  room 
to  put  the  arm  in. 


OF  CONSTRUCTING  WHEELS.  -319 

ART.    13. 
TO  PUT  IN  THE  GUDGEONS. 

Strike  a  circle  on  the  ends  of  the  shaft  to  let  on  the  end 
bands  ;  make  a  circle  all  round  2  1-2  feet  from  each  end, 
and  saw  a  notch  all  round  half  an  inch  deep.  Lay  out  a 
square  round  the  centres  the  size  of  the  gudgeons,  near 
the  neck  ;  lay  the  gudgeons  straight  on  the  shaft,  and 
scribe  round  them  for  their  mortises ;  let  them  down 
within  1-8  of  an  inch  of  being  in  the  centre.  Dress  off 
the  ends  to  suit  the  bands  ;  make  3  keys  of  good  season- 
ed white  oak,  to  fill  each  mortise  above  the  gudgeons, 
to  key  them  in,  those  next  to  the  gudgeons  to  be  3  i-i 
inches  deep  at  their  inner  end,  and  11-2  inch  at  their 
outer  end,  the  wedge  or  driviug  key  3  inches  at  the  head, 
and  6  inches  longer  than  the  mortise,  that  it  may  be  cut 
off  if  it  batters  in  driving ;  the  piece  next  the  band  so 
wide  as  to  rise  half  an  inch  above  the  shaft,  when  all  are 
laid  in.  Then  take  out  all  the  keys  and  put  on  the 
bands,  and  make  8  or  12  iron  wedges  about  4  inches 
long  by  2  wide,  1-3  inch  thick  at  the  end,  not  much  ta- 
pered except  half  an  inch  at  the  small  end,  on  one  side 
next  the  wood  ;  drive  them  in  on  each  side  the  gudgeon 
exceeding  hard  at  a  proper  distance  with  a  set.  Then 
put  in  the  k6ys  again,  and  lay  a  piece  of  iron  under  each 
band  between  it  and  the  key  6  inches  long,  half  an  inch 
thick  in  the  middle,  and  tapering  off  at  the  ends  ;  then 
grease  the  keys  well  with  tallow  and  drive  it  well  with 
a  heavy  sledge  :  after  this  drive  an  iron  wedge  half  an 
inch  from  the  two  sides  of  each  gudgeon  5  inches  long, 
near  half  an  inch  thick,  and  as  wide  as  tl^e  gudgeon. 


ART.     14. 

OF  COG-WHEELS. 

The  great  face  cog-wheels  require  8  (called  6)  arms, 
if  the  number  of  cogs  exceed  54,  if  less  4  will  do.     We 


320  OF  CONSTRUCTING  WHEELS. 

find  by  the  table,  example  43,  that  the  cog-wheel  must 
have  69  cogs,  with  4  1-2  inches  pitch,  the  diameter  of 
its  pitch  circle  8  feet  2  1-3  inches,  and  of  its  outsides  8 
feet  10  1-3  inches.  It  requires  3  arms  9  feet  long,  14 
by  3  3-4  inches ;  12  cants  6  1-2  feet  long,  16  by  4  in- 
ches.    See  it  represented  plate  XVII,  fig.  1. 

To  frame  it,  dress  and  lock  the  arms  together,  as  fig. 
6)  as  directed  art.  10,  only  mind  to  leave  1-3  of  each 
arm  uncut,  and  to  lock  them  the  right  way  to  suit  the 
winding  ©f  the  mortises  in  the  shaft,  which  is  best  found 
by  putting  a  strip  of  board  in  the  middle  mortise,  and 
supposing  it  to  be  the  arm,  mark  which  way  it  should 
be  cut,  then  apply  the  board  to  the  arm,  and  mark  it. 
The  arms  being  laid  on  a  truckle  as  directed  art.  10, 
triake  a  sweep  the  sides  directing  to  the  centre,  2  feet 
from  the  out  end  to  scribe  by ;  measure  on  the  sweep 
half  the  diameter  of  the  wheel,  and  by  it  circle  out  the 
back  edges  of  the  cants,  all  of  one  width  in  the  mid- 
dle ;  dress  them,  keeping  the  best  faces  for  the  face  side 
of  the  wheel ;  make  a  circle  on  the  arms  1-2  an  inch 
larger  than  the  diameter  of  the  wheel,  laying  3  of  the 
cants  with  their  ends  on  the  arms  at  this  circle  at  equal 
distance  apart.  Lay  the  other  three  on  the  top  of  them, 
so  as  to  lap  equally,  scribe  them  both  under  and  top, 
and  gauge  all  for  the  laps  from  the  face  side  ;  dress 
them  out  and  lay  them  together,  and  joint  them  close  ; 
draw-pin  them  by  an  inch  pin  near  their  inside  corners  : 
this  makes  one  half  of  the  wheel  shown  fig.  5.  Raise 
the  centre  level  with  that  half,  strike  a  circle  near  the 
outside  and  find  the  centre  of  one  of  the  cants  ;  then, 
with  the  sweep  that  described  the  circle,  step  on  the  cir- 
cle 6  steps,  beginning  at  the  middle  of  the  cant,  and  these 
steps  will  show  the  middle  of  all  the  cants  or  places  for  the 
arms.  Make  a  scribe  from  the  centre  across  each;  strike 
another  circle  exactly  at  the  corners,  to  place  the  corners 
of  the  next  half  by,  and  another  about  2|  inches  farther 
out  than  the  inside  of  the  widest  part  of  the  cant,  to  let  the 
arms  in  by ;  lay  on  three  of  the  upper  cants,  the  widest 
part  over  the  narrowest  part  of  the  lower  half,  the  inside 
to  be  at  the  point  where  the  corner  circle  crosses  the  cen- 
tre lines.     Saw  off  the  ends  at  the  centre  scribes,  and  fit 


OF  CONSTRUCTING  WHEELS.  321 

them  down  to  their  places,  doing  the  same  with  the  rest. 
Lay  them  all  on,  and  joint  their  ends  together ;  draw  pin 
them  to  the  lower  half  by  inch  pins,  2  inches  from  their 
inmost  edges,  and  9  inches  from  their  ends.  Raise  the 
centre  level  with  the  wheel;  plane  a  litde  of  the  rough  off 
the  face,  and  strike  the  pitch  circle  and  another  4  inches 
inside  for  the  width  of  the  face;  strike  another  very  neav 
it,  in  which  drive  a  chisel  half  an  inch  deep  all  round, 
and  strike  lines  with  chalk  in  the  middle  of  the  edge  of 
the  upper  cants,  and  cut  out  of  the  solid  half  of  the  up- 
per cants,  which  raises  the  face ;  divide  the  pitch  circle 
into  69  equal  parts,  4|  inches  pitch,  beginning  and 
ending  in  a  joint;  strike  two  other  circles  each  2  1-2 
inches  from  the  pitch  circle,  and  strike  central  scribes 
between  the  cogs,  and  where  they  cross  the  circles  put 
in  pins,  as  many  as  there  are  cogs,  half  on  each  circle; 
find  the  lowest  part  on  the  face,  and  make  the  centre  le- 
vel Mith  it;  look  across  in  another  place  square  with 
the  first,  and  make  it  level  with  the  centre  also ;  then 
make  the  face  straight  from  these  4?  places,  and  it  will 
be  true. 

Strike  the  pitch  circle,  and  divide  it  over  again,  and  one 
of  each  side  of  it,  1  inch  distance  for  the  cog  mortises; 
sweep  the  outside  of  the  wheel  and  inside  of  the  face,  and 
two  circles  3-4  of  an  inch  from  them,  to  dress  off  the  cor- 
ners ;  strike  a  circle  of  two  inches  diameter  on  the  centre 
of  each  cog,  and  with  the  sweep  strike  central  scribes 
at  each  side  of  these  circles  for  the  cog  mortises ;  bore 
and  mortise  half  through ;  turn  the  wheel,  dress  and  mor- 
tise the  back  side,  leaving  the  arms  from  under  it ;  strike 
a  circle  on  the  face  edge  of  the  arms,  equal  in  diameter 
to  that  struck  on  the  face  of  the  half  wheel,  to  let  them 
in  by;  saw  in  square  and  take  out  4|  inches,  and  let 
them  into  the  back  of  the  wheel  11-4  inch  deep,  and 
bore  a  hole  11-2  inch  into  each  arm,  to  pin  it  to  the 
wheel. 

Strike  a  circle  on  the  arms  one  inch  less  than  the  dia- 
meter of  the  shaft,  make  a  key  8  inches  long.  If  thick, 
3 1  at  the  butt,  and  2|  inches  at  the  top  end,  and  by  it  lay 
out  the  mortises ;  two  on  each  side  of  the  shaft,  in  each 
arm  to  hang  the  wheel  by. 

s   s 


gl2  OF  SILLS,  SPUR-BLOCKS,  &c. 

ART.    15. 

OF  SILLS,  SPUR-BLOCKS,  AND  HEAD-BLOCKS. 

See  a  side  view  of  them  in  plates  XIII,  XIV,  XV,  and 
XVI,  and  a  top  view  of  them  with  their  keys  at  the  end 
of  the  shaft,  plate  XVIII.  The  sills  are  generally  12 
inches  square.  Lay  them  on  the  wall  as  firm  as  possible^ 
and  one  3  feet  farther  out,  on  these  lay  the  spurs,  which 
are  5  feet  long,  7  by  7  inches,  3  feet  apart,  notched  and 
pinned  to  the  sills ;  on  these  are  set  the  head-blocks,  14  by 
12  inches,  5  feet  long,  let  down  with  a  dove-tail  shoulder 
between  the  spurs,  to  support  keys  to  move  it  endways, 
and  let  2  inches  into  the  spurs  with  room  for  keys,  to  move 
it  sideways,  and  hold  it  to  its  place ;  see  fig.  33  and  34*, 
plate  XVIII.  The  ends  of  the  shaft  are  let  2  inches  into 
the  head- blocks,  to  throw  the  weight  more  on  the  centre. 

Provide  two  stones  5  or  6  inches  square,  very  hard 
and  clear  of  grit,  for  the  gudgeons  to  run  on,  let  them 
into  the  head-blocks,  put  the  cog-wheel  into  its  place, 
and  then  put  in  the  shaft  on  the  head-blocks  in  its  place. 

Put  in  the  cog-wheel  arm,  lock  them  together  and  pin 
the  wheel  to  them ;  then  hang  the  wheel  first  by  the  keys, 
to  make  it  truly  round,  and  then  by  side  wedges,  to 
make  it  true  in  face ;  turn  the  wheel,  and  make  two  cir- 
cles one  on  each  side  of  the  cog-mortises,  half  an  inch 
from  them,  so  that  the  head  of  the  cogs  may  stand  be- 
tween them  equally. 


ART.    16, 

OF  COGS;  THE  BEST  TIVIE  FOR  CUTTING,  AND  WAY  OF  SEA- 
SONING THEM. 

They  should  be  cut  14  inches  long,  3  1-4  inches 
square,  when  the  sap  runs  at  its  fullest,  which  should  be 
done  at  least  a  year  before  they  are  used,  that  they  may 
dry  without  cracking.  If  either  hickory  or  white-oak  is 
cut  when  the  bnrk  is  set,  they  will  worm-eat,  and  if 
dried  hastily,  will  crack ;   to  prevent  which,  boil  them 


*  OF   COGS.  32^ 

and  dry  them  slowly,  or  soak  them  in  water,  a  year,  (SO 
years  in  mud  and  fresh  water  would  not  hurt  them  ;) 
when  they  are  taken  out  they  should  be  put  in  a  hay- 
Ynow  under  the  hay,  which  when  foddered  away  they 
will  dry  without  cracking ;  but  this  often  takes  too  long 
time.  I  have  discovered  the  following  method  of  dry- 
ing them  in  a  few  days  without  cracking :  I  have  a  malt- 
kiln  with  a  floor  of  laths  two  inches  apart.  I  shank  the 
cogs,  hang  them  shank  downwards,  between  the  laths 
cover  them  with  a  hair-cloth,  make  a  wood  fire,  and  the 
smoke  preserves  them  from  cracking.  Some  dry  them 
in  an  oven,  which  ruins  them.  Boards,  planks,  or 
scantling  are  best  dried  in  a  kiln,  covered  so  as  to  keep 
the  smoke  amongst  them.  Instead  of  a  malt  kiln,  dig 
a  cave  in  the  side  of  a  hill,  6  feet  deep,  5  or  6  feet  wide, 
with  a  post  in  each  corner  with  plates  on  them,  on 
which  lay  laths  on  edge,  and  pile  the  cogs  on  end  near- 
ly perpendicular,  so  that  the  smoke  can  pass  freely 
through  or  amongst  them.  Cover  slighdy  with  boards 
and  earth,  make  a  slow  fire  and  close  up  the  sides,  and 
renew  the  fire  once  a  day  for  12  or  15  days,  they  will 
dry  without  cracking.  Experienced  by  James  Dellet, 
Mill-wright. 


ART.    17. 

OF  SHANKING,  PUTTING  IN,  AND  DRESSING  OFF  COGS. 

Straighten  one  of  the  heart  sides  for  the  shank,  make  a 
pattern,  the  head  4  and  shank  10  inches  long,  and  2  inches 
wide  at  the  head,  1|  at  the  point;  lay  it  on  the  cog, 
scribe  the  shank  and  shoulders  for  the  head,  saw  in  and 
dress  off  the  sides  ;  make  another  pattern  of  the  shank, 
without  the  head,  to  scribe  the  sides  and  dress  off  the 
backs  by,  laying  it  even  with  the  face,  which  is  to  have  no 
shoulder ;  take  great  care  in  dressing  them  off,  that  thq 
axe  does  not  strike  the  shoulder,  if  it  does  it  will  crack 
there  in  drying  (if  they  be  green)  ;  fit  and  drive  them  in 
the  mortises  exceeding  tight,  with  their  shoulders  fore- 
most when  at  work.     When  the  cogs  are  all  in,  fix  two 


324  OF  THE  LITTLE  COG  WHEEL  AND  SHAFT 

pieces  of  scantling  for  rests,  to  scribe  the  cogs  by,  one 
across  the  cog-pit  near  the  cogs,  another  in  front  of  them, 
fix  them  firm.  Hold  a  pointed  tool  on  the  rest,  and 
scribe  for  the  length  of  the  cogs  b}^  turning  the  wheel, 
and  saw  them  off  3|  inches  long ;  then  move  the  rest 
close  to  them,  and  fix  it  firm ;  find  the  pitch  circle  on 
the  end  of  the  cogs,  and  by  turning  the  wheel  describe 
it  there. 

Describe  another  |  of  an  inch  outside  thereof,  to  set 
the  compass  in  to  describe  the  face  of  the  cogs  by,  and 
another  at  each  side  of  the  cogs  to  dress  them  to  their 
width  :  then  pitch  the  cogs  by  dividing  them  equally,  so 
that  in  stepping  round,  the  compasses  may  end  in  the 
point  wiiere  they  began  ;  describe  a  circle  in  some  par- 
ticular place  with  the  pitch  that  it  may  not  be  lost ;  these 
points  must  be  as  near  as  possible,  of  a  proper  distance 
for  the  centre  from  the  back  of  the  cogs ;  find  the  cog 
that  this  point  comes  nearest  to  the  back,  and  set  the 
compasses  from  that  point  to  the  back  of  the  cog,  and 
with  this  distance  set  off  the  backs  of  all  the  cogs  equal- 
ly, on  the  circle  1-4  of  an  inch  outside  of  the  pitch  cir- 
cle, and  from  these  points  last  made,  set  off  the  thick- 
ness of  the  cogs,  which  should  be  2  1-8  inches  in  this 
case. 

Then  describe  the  face  and  back  of  the  cogs  by  setting 
the  compasses  in  the  hindmost  point  of  one  cog,  and 
sweeping  over  the  foremost  point  of  another  for  the  face, 
and  in  the  foremost  point  of  one,  sweeping  over  the  hind- 
most of  the  other,  for  the  back  part ;  dress  them  ofi"  on 
all  sides,  tapering  about  1-8  of  an  inch  in  an  inch  dis- 
tance, try  them  by  a  gauge  to  make  them  all  alike,  take 
a  little  of  the  corners  off,  and  they  are  finished. 


ART.     18. 
OF  THE  LITTLE  COG-WHEEL  AND  SHAFT. 

The  process  of  making  this  is  similar  to  that  of  the  big 
cop;- wheel-  Its  dimensions  we  find  by  the  table,  and  the 
same  example  43,  to  be  52  cogs,  4  1-4  pitch.  Diameter 
of  pitch  circle  5  feet  10  1-3  inches,  and  from  out  to  out 
6  feet  6  inches. 


OF  WALLOWERS  AND  TRUNDLES.       325 

It  requires  3  arms  6  feet  6  inches  long,  11  by  3| 
inches;  8  cants  f>  feet  6  inches,  17  by  3|  inches.  See 
it,  plate  XVII,  fig.  4. 

Of  the  Shaft. 

Dress  it  8  feet  long,  14  by  14  square,  and  describe  a 
circle  on  each  end  14  inches  diameter;  strike  two  lines 
through  the  centre  parallel  to  the  sides,  and  divide  the 
quarters  into  4  equal  parts  each ;  strike  lines  across  the 
centre  at  each  part  at  the  end  of  these  lines ;  strike  chalk 
lines  from  end  to  end  to  hew  off  the  corners  by,  and  it 
will  be  8  square ;  lay  out  the  mortises  for  the  arms,  put 
on  the  bands,  and  put  in  the  gudgeons,  as  with  the  big 
shaft. 


ART.    19. 
DIRECTIONS  FOR  MAKING  WALLOWERS  AND  TRUNDLE^. 

By  example  43  in  the  table,  the  wallower  is  to  have 
26  rounds  4|  pitch.  Diameter  of  its  pitch  circle  is  3 
feet  1|  inch,  and  3  feet  4|  inches  from  outsides:  see 
fig.  3.  plate  XVII.  Its  head  should  be  3^  inches  thick, 
doweled  truly  together,  or  made  double  with  plank  cross- 
ing each  other.  Make  the  bands  three  inches  wide,  1-6 
of  an  inch  evenly  drawn;  the  heads  must  be  made  to 
suit  the  bands,  by  setting  the  compasses  so  that  they 
will  step  round  the  inside  of  the  band  in  6  steps;  with 
this  distance  sweep  the  head,  allowing  about  1-16  of  an 
inch  outside  in  dressing  to  make  such  a  large  band  tiojht. 
Make  them  hot  alike  all  round  with  a  chip  fire,  which 
swells  the  iron;  put  them  on  the  head  while  hot,  and 
cool  them  with  water  to  keep  them  from  burning  the 
wood  too  much,  but  not  too  fast  lest  they  snap :  the  same 
for  hooping  all  kinds  of  heads. 

Dress  the  head  fair  after  banded,  and  sti-ike  the  pitch 
circle  and  divide  it  by  the  same  pitch  of  the  cogs ;  bore 
the  holes  for  the  rounds  with  an  auger  at  least  1 1  inch ; 
make  the  roimds  of  the  best  wood  2  3-8  inches  diame- 


m  OF  HANGING  WHEELS,  he. 

ter,  and  1 1  inches  between  the  shoulders,  the  tenons  4 
inches,  to  fit  the  holes  loosely  until  within  1  inch  of  the 
shoulder,  then  drive  tight.  Make  the  mortises  for  the 
shaft  in  the  heads,  with  notches  for  the  keys  to  hang  it 
by.  When  the  rounds  are  ajl  drove  in  to  the  shoulders, 
observe  whether  they  stand  straight,  if  not,  they  may  be 
set  fair  by  putting  the  wedges  nearest  to  one  side  of  the 
tenon,  so  that  the  strongest  part  may  incline  to  draw  them 
straight :  this  should  be  done  with  both  heads. 


ART.    20. 

OF  FIXING  THE  HEAD  BLOCKS   AND  HANGING  THE  WHEELS. 

The  head  blocks  for  the  wallower  shaft,  are  shown  in 
plate  XVIII.  Number  19  is  one  called  a  spur,  6  feet 
long  and  15  inches  deep,  one  end  of  which  at  19  is  let 
one  inch  into  the  top  of  the  husk-sill,  which  sill  is  1|  inch 
above  the  floor,  the  other  end  tenoned  strongly  into  a 
strong  post  14  by  14  inches,  12  or  14  feet  long,  standing 
near  the  cog- wheel  on  a  sill  in  the  bottom  of  the  cog- pit; 
the  top  is  tenoned  into  the  husk-plank;  these  are  called 
the  tomkin  posts.  The  other  head-blocks  appear  at  20 
and  38.  In  these  large  head-blocks  there  are  small  ones 
let  in,  that  are  3  feet  long  and  6  inches  square,  with  a 
stone  in  each  for  the  gudgeons  to  run  on.  That  one  in 
the  spur  19  is  made  to  slide,  to  put  the  wallower  out  and 
in  gear  by  a  lever  screwed  to  its  side. 

Lay  the  centre  of  the  little  shaft  level  with  the  big 
one,  so  as  to  put  the  wallower  to  gear  2-3  the  thickness 
of  the  rounds  deep  into  the  cog-wheel;  put  the  shaft 
into  its  place  and  hang  the  wallower,  and  gauge  the 
rounds  to  equal  distance  where  the  cogs  take.  Hang  the 
cog-wheel,  put  in  the  cogs,  make  the  trundle  as  directed 
for  the  wallower.     See  plate  XVII,  fig.  4. 


ART.    Si. 
DIRECTIONS  FOR  PUTTING  IN  THE  BALANCERYNE. 

Lay  it  in  the  eye  of  the  stone,  and  fix  it  truly  in  the 
centre ;  to  do  which  make  a  sweep  by  putting  a  long  pin 


OF  SINKING  THE  BALANCE-RYNE.         S2? 

through  the  end  to  reach  into  and  fit  the  pivot  hole  in 
the  balance  ryne ;  by  repeated  trials  on  the  opposite  sides 
fix  it  in  the  centre  ;  then  make  a  particular  mark  on  the 
sweep  and  others  to  suit  it  on  the  stone,  scribe  round 
the  horns,  and  with  picks  and  chisels  sink  the  mortises 
to  their  proper  depth,  trying  by  the  sweep  if  it  be  in  the 
centre,  by  the  particular  marks  made  for  the  purpose. 
Put  in  the  spindle  with  the  foot  upwards  and  the  driver 
on  its  place,  while  one  holds  it  plumb.  Set  the  driver 
over  two  of  the  horns,  if  it  has  four,  but  between  them 
if  it  has  but  two.  When  the  neck  is  exactly  in  the  cen- 
tre of  the  stone,  scribe  round  the  horns  of  the  driver, 
and  let  it  into  the  stone,  nearly  to  the  balance,  if  it  has 
four  horns.  Put  the  top  of  the  spindle  in  the  pivot-hole 
to  try  whether  the  mortses  let  it  down  freely  on  both 
sides. 

Make  a  tram  to  set  the  spindle  square  by,  as  follows : 
take  a  piece  of  board,  cut  a  notch  in  one  side,  at  one 
end,  and  hang  it  on  the  top  of  the  spindle,  by  a  little  peg 
in  the  shoulder  of  the  notch,  to  go  in  the  hole  in  the 
foot  to  keep  it  on,  let  the  other  end  reach  down  to  the 
edge  of  the  stone,  take  another  piece,  circle  out  one  end 
to  fit  the  spindle  neck,  and  make  the  other  end  fast  to 
the  lower  end  of  the  hanging  piece  near  the  stone,  so  as 
to  play  round  level  with  the  face  of  the  stone,  resting  on 
the  centre-hole  in  the  foot,  and  against  the  neck,  put  a 
bit  of  quill  through  the  end  of  the  level  piece,  that  will 
touch  tlie  edge  of  the  stone  as  it  plays  round.  Make 
litde  wedges  and  drive  them  in  behind  the  horns  of  the 
driver,  to  keep  both  ends  at  once  close  to  the  sides  of 
the  mortises  they  bear  against  when  at  work,  keeping 
the  pivot  or  cock-head  in  its  hole  in  the  balance,  try  the 
tram  gently  round,  and  mark  where  the  quill  touches  the 
stone  first,  and  dress  off"  the  bearing  sides  of  the  mortises 
for  the  driver  until  it  will  touch  equally  round,  giving 
the  driver  liberty  to  move  endways  and  sideways  to  let 
the  stone  rock  an  inch  any  way.  The  ryne  and  driver 
must  be  sunk  3-4  of  an  inch  below  the  face  of  the  stone. 
Then  hang  the  trundle  firmly  and  truly  on  the  spindle, 
put  it  in  its  place  to  gear  in  the  little  cog-wheel. 


'S28  OF  BRIDGING  THE  SPINDLE,  &c. 


ART.   S2. 

TO  BRIDGE  THE  SPINDLE. 

Make  a  little  tram  of  a  piece  of  lath,  3  inches  wide  at 
one  end,  and  1  inch  at  the  other,  make  a  mortise  in  the 
wide  end,  and  put  it  on  the  cock-head,  and  a  piece  of 
quill  in  the  small  end,  to  play  round  the  face  of  the  stone  : 
then,  while  one  turns  the  trundle,  another  observes  where 
the  quill  touches  first,  and  alters  the  keys  of  the  bridge- 
tree,  driving  the  spindle-foot  toward  the  part  the  quill 
touches,  until  it  touches  equally  all  round.  Case  the 
stone  neatly  round  within  2  inches  of  the  face-. 


ART.    23. 
OF  THE  CRANE  AND  LIGHTER-STAFF. 

Make  a  crane  for  taking  up  and  putting  down  the  stone, 
with  a  screw  and  bale.  See  it  represented  in  Evans's 
part,  pi.  XI.  fig.  2  and  3.  Set  the  post  out  of  the  way  as 
much  as  possible,  let  it  be  9  by  6  inches  in  the  middle,  the 
arm  9  by  6,  brace  6  by  4,  make  a  hole  plumb  over  the 
spindle,  for  the  screw,  put  an  iron  washer  on  the  arm 
under  the  female  screw,  nail  it  fast,  the  screw  should  be 
above  half  the  diameter  of  the  stone,  in  the  worm,  and 
10  inches  below  it,  the  bale  to  touch  only  at  the  ends  to 
give  the  stone  liberty  to  turn,  the  pins  to  be  7  inches  long, 
11-8  thick,  the  bale  to  be  2|  inches  wide  in  the  middle, 
and  1|  inch  wide  at  the  end ;  all  of  the  best  iron,  for 
if  either  of  them  break  the  danger  would  be  great.  The 
holes  in  the  stone  should  be  nearest  the  upper  side  of 
it.  Raise  the  runner  by  the  crane,  screw  and  bale,  turn 
it  and  lay  it  down,  with  the  horns  of  the  driving  ryne  in 
their  right  places,  as  marked,  it  being  down,  as  appears 
in  pi.  XXI.  fig.  9.  Make  the  lighter-staff  C  C  to  raise 
and  lower  the  stone  in  grinding,  about  6  feet  long,  3| 
by  21  inches  at  the  large  end,  and  2  inches  square  at 
the  small  end,  with  a  knob  on  the  upper  side.  Make  a 
mortise  through  the  butt  end  for  the  bray-iron  to  pass 


OF  MAKING  A  HOOP  FOR  THE  MILL-STONE.  329 

throus^h,  which  goes  into  a  mortise  4  inches  deep  in  the 
end  of  the  bray  at  b,  and  fastened  with  a  pin;  it  may  be 
2  inches  wide,  half  an  inch  thick,  a  plain  bar  with  one 
hole  at  the  lower  end,  and  5  or  6  at  the  upper  end,  set  in 
a  staggering  position.  This  lighter  is  fixed  in  front  of  the 
meal-beam,  at  a  proper  height  to  be  handy  to  raise  or 
lower  at  pleasure ;  a  weight  of  4  lb.  is  hung  to  the  end  of 
it  by  a  strap,  that  laps  two  or  tliree  times  round,  and  the 
other  end  fastened  to  the  post  below,  that  keeps  it  in  its 
place.  Play  the  lighter  up  and  down,  and  observe  whe- 
ther the  stone  rises  and  falls  flat  on  the  bed-stone,  if  it 
does,  draw  a  litde  water,  and  let  the  stone  move  gently 
round,  then  see  that  all  things  be  right,  and  draw  a  little, 
more  water,  let  the  stone  run  at  a  middling  rate,  and 
grind  the  faces  a  few  minutes. 


ART.    S4. 
DIRECTIONS  FOR  MAKING  A  HOOP  FOR  THE  MILL  STONE. 

Take  a  white  pine  or  poplar  board,  8  inches  longer 
than  will  go  round  the  stone,  and  2  inches  wider  than 
the  top  of  the  stone  is  high,  dress  it  smooth,  and  gauge 
it  one  inch  thick,  run  a  gauge  mark  1-6  of  an  inch  from 
the  outside,  divide  the  length  into  52  parts,  and  saw  as 
many  saw- gates  square  across  the  inside  to  the  gauge - 
line.  Take  a  board  of  equal  width,  1  foot  long,  nail  one 
half  of  it  on  the  outside  at  one  end  of  the  hoop,  lay  it 
in  water  a  day  or  two  to  soak,  or  sprinkle  the  outside 
well  an  hour  or  two  with  hot  water.  Bend  it  round  so 
that  the  ends  meet,  and  nail  the  other  end  to  the  short 
board,  put  sticks  across  inside  in  every  direction  to  press 
out  the  parts  that  bend  least,  and  make  it  truly  round. 
Make  a  cover  for  the  hoop,  such  as  is  represented  in 
plate  XIX,  fig.  23,  8  square  inside,  and  1  inch  outside 
the  hoop.  It  consists  of  8  pieces  lapped  over  one  ano- 
ther, the  black  lines  showing  the  joints  as  they  appear 
when  made,  the  dotted  lines  the  under  parts  of  the  laps. 
Describe  it  on  the  floor,  and  make  a  pattern  to  make  all 

T  t 


330  OF  FACING  STONES,  Sec. 

the  rest  by ;  dress  all  the  laps,  fit  and  nail  them  to,8jether 
b}'  the  circle  on  the  floor,  and  then  nail  it  on  the  h>')p; 
put  the  hoop  over  the  stone  and  scribe  it  to  fit  the  floor 
in  its  place. 


ART.     25. 

OF  GRINDING  SAND  TO  F'\CE  THR  STONES. 

Lay  boards  over  the  hoop  to  keep  the  dust  from  fly- 
ing, and  take  a  bushel  or  two  of  dry,  clean,  sharp  sand, 
teem  it  gently  in  the  eye,  while  the  stones  move  at  a 
moderate  rate,  continuing  to  grind  for  an  hour  or  two ; 
then  take  up  the  stones,  sweep  them  clean,  and  pick  the 
smoothest  hardest  places,  and  lay  the  stone  down  again, 
and  grind  more  sand  as  before,  turning  off"  the  back,  (if 
it  be  a  bun-)  taking  great  care  that  the  chisel  does  not 
catch ;  take  up  the  stone  again,  and  make  a  red  staff",  i» 
length  the  diameter  of  the  stone,  3  by  2 1  inches,  paint  it 
with  red  paint  and  water,  and  rub  it  over  the  face  of  the 
stones  in  all  directions,  the  red  will  be  left  on  the  highest 
and  hardest  parts,  which  must  be  pecked  down,  making 
the  bed-stone  perfectly  plain,  and  the  runner  a  little  con- 
cave about  1-6  of  an  inch  at  the  eye,  and  lessening  gra- 
dually to  about  8  inches  from  the  skirt.  If  they  be  close 
and  have  much  face  they  need  not  touch  or  flour  so  far, 
as  if  they  are  open  and  have  but  little  face;  those  things 
are  left  to  the  judgment  of  the  mill-wright  and  miller. 


ART.    26. 

DIRECTIOXS  FOR  LAYING  OUT  THE  FURROWS  IN  THE 
STONES,  &c. 

If  they  be  five  feet  in  diameter,  divide  the  skirt  into 
16  equal  parts,  called  quarters,  if  6  feet,  into  18,  if  7 
feet,  into  20  quarters.  Make  two  strips  of  board,  one 
an  inch,  and  the  other  2  inches  v\  ide :  stand  with  your 
face  to  the  eye,  and  if  the  stone  turns  to  the  right  when 
at  work,  lay  the  strip  at  one  of  the  quarter  divisions,  and 
the  other  at  the  left  hand  side  close  to  the  eye,  and  mark 


OF  FURROWING  STONES.  331 

with  a  flat  pointed  spike  for  a  master  furrow  ;  they  all 
are  laid  out  the  same  way  in  both  stones,  for  when  their 
faces  are  together,  the  furrows  should  cross  each  other  like 
shears  in  the  best  position  for  cutting  cloth.  Then,  hav- 
ing not  less  than  6  good  picks,  proceed  to  pick  out  all 
the  master  furrows,  making  the  edge  next  the  skirt  and 
the  end  next  the  eye  the  deepest,  the  feather  edge  not 
half  so  deep  as  the  back. 

When  all  the  master  furrows  are  picked  out,  lay  the 
broad  strip  next  to  the  feather  edges  of  all  the  furrows, 
and  mark  the  head  lands  of  the  short  furrows,  then  lay 
the  same  strip  next  the  back  edges,  and  mark  for  the 
lands,  and  lay  the  narrow  strip,  and  mark  for  the  fur- 
rows, and  so  on  mark  out  all  the  lands  and  furrows, 
minding  not  to  cross  the  head  lands,  but  leaving  it  be- 
tween the  master  furrows  and  the  short  ones  of  each 
quarter.  But  if  they  be  close  country  stones,  lay  out 
both  furrows  and  land  with  the  narrow  strip. 

The  neck  of  the  spindle  must  not  be  wedged  too  tight 
else  it  will  burn  loose ;  bridge  the  spindle  again  ;  put  a 
collar  round  the  spindle  neck,  but  under  it  put  a  piece 
of  an  old  stocking,  with  tallow  rolled  up  in  it,  about  a 
finger  thick ;  tack  it  close  round  the  neck  ;  put  a  piece 
of  stiff  leather  about  6  inches  diameter  on  the  cock-head 
under  the  driver,  to  turn  with  the  spindle  and  drive  off 
the  grain,  &c.  from  the  neck  ;  grease  the  neck  with  tal- 
low every  time  the  stone  is  up. 

Lay  the  stone  down  and  turn  off  the  back  smooth, 
and  grind  more  sand.  Stop  the  mill ;  raise  the  stone  a 
little,  and  balance  it  truly  with  weight  laid  on  the  light- 
est side.  Take  lead  equal  to  this  weight,  melt  it,  and 
run  it  into  a  hole  made  in  the  same  place  in  the  plaister, 
largest  at  bottom  to  keep  it  in,  fill  the  hole  with  plaister, 
take  up  the  runner  again,  try  the  staff  over  them,  and  if 
in  good  face  give  them  a  nice  dressing,  and  lay  them 
down  to  grind  wheat. 


^2    OF  THE  HOPPER,  SHOE,  AND  FEEDER. 


ART.   S7. 

DIRECTIONS  FOR  MAKING  A  HOPPER,  SHOE,  AND  FEEDER. 

The  dimension  of  the  hopper  of  a  common  mill  is  4 
feel  at  the  top,  and  2  feet  deep,  the  hole  in  the  bottom  3 
inches  square,  with  a  sliding  gate  in  the  bottom  of  the 
front  to  lessen  it  at  pleasure  :  the  shoe  10  inches  long, 
and  5  wide  in  the  bottom,  of  good  sound  oak.  The  side 
7  or  8  inches  deep  at  the  hinder  end,  3  inches  at  the 
foremost  end,  6  inches  longer  than  the  bottom  at  the 
fore  end,  slanting  more  than  the  hopper  behind,  so  that 
it  may  ha\  e  liberty  to  hang  down  3  or  4  inches  at  the 
fore  end,  which  is  hung  by  a  strap  called  the  feeding- 
string,  passing  over  the  fore  end  of  the  hopper-frame, 
and  lapping  round  a  pin  in  front  of  the  meal-beam,  that 
will  turn  by  the  hand,  called  the  feeding- screw. 

The  feeder  is  a  piece  of  wood  turned  in  a  lathe,  about 
20  inches  long,  3  inches  diameter  in  the  middle  against 
the  shoe,  tapered  oft'  to  1|  inches  at  the  top  ;  the  lower 
end  is  banded  and  a  forked  iron  drove  in  it,  that  spans 
over  the  ryne  fitting  into  notches  made  on  each  side,  to 
receive  it,  right  above  the  spindle,  and  turns  with  it ;  the 
upper  end  running  in  a  hole  in  a  piece  across  the  hop- 
per-frame. In  the  large  part  next  the  shoe  are  set  6 
iron  knockers,  7  inches  long,  half  an  inch  diameter,  with 
a  tang  at  each  end,  turned  square  to  drive  into  the  wood, 
these  knock  against,  and  shake  tlie  shoe,  and  thereby 
shake  in  the  grain  regularly. 

Then  put  grain  into  the  hopper,  draw  water  on  the 
mill,  regulate  the  feed  by  turning  the  feed-screw,  until 
the  stream  falling  into  the  eye  of  the  stone,  is  propor- 
tioned to  the  size  thereof,  or  the  power  of  the  mill.  Here 
ends  the  mill-wright's  work,  with  respect  to  grinding, 
and  the  miller  takes  charge  thereof. 


ART.  S8. 
OF  BOLTING  CHESTS  AND  REELS. 

Bolting-chests  and  reels  are  of  different  lengths,  accord- 
ing to  the  use  they  are  for.     Common  country  chests  (a 


OF  BOLTING-CHESTS  AND  REELS.        333 

top  view  of  one  of  which  is  shown,  pi.  VIL  fig.  9,)  are 
commonly  about  10  feet  long,  3  feet  wide,  and  7  feet  -t 
inches  high,  with  a  post  in  each  corner,  the  bottom  3  feet 
from  the  floor,  with  a  board  18  inches  wide,  set  slanting 
in  the  back  side,  to  cast  the  meal  forward  in  the  chest, 
to  make  it  easily  taken  up  ;  the  door  of  the  whole  length 
of  the  chest,  and  two  feet  wide,  the  bottom  side  board 
below  the  door  16  inches  wide. 

The  shaft  of  the  reel  equal  in  length  with  the  chest,  4j 
inches  diameter,  6  square,  two  bands  on  each  end,  3  1-4) 
and  3  3-4  diameter,  gudgeons  13  inches  long,  7-8  of  an 
inch  diameter ;  8  inches  in  the  shaft,  round  g  1-2  inches 
at  the  neck,  with  a  tenon  for  a  socket  or  handle,  six  ribs 
112  inch  deep,  1  1-8  inch  thick,  half  an  inch  shorter  at 
the  tail,  and  1  1-S  inch  at  the  head,  than  the  shaft,  to  leave 
room  for  the  meal  to  be  spouted  in  at  the  head,  and  the 
bran  to  fall  at  the  tail ;  four  sets  of  arms,  that  is,  12  of 
them,  11-3  inch  wide,  and  5-8  thick.  The  diameter  of 
the  reel  from  out  to  out  of  the  ribs,  is  one-third  part  of 
the  double  width  of  the  cloth.  A  round  wheel  of  inch 
boards,  and  diameter  equal  to  the  outside  of  the  ribs,  4| 
inches  wide,  measuring  from  the  outside  towards  the 
centre,  (which  is  taken  out)  is  to  be  framed,  to  the  head 
of  the  reel,  to  keep  the  meal  from  falling  out  at  the  head 
unbolted.  Put  a  hoop  4|  inches  wide,  and  ^  thick,  round 
the  tail,  to  fasten  the  cloth  to.  The  cloth  is  sewed  two 
widths  of  it  together,  to  reach  round  the  reel ;  putting  a 
strip  of  sti'ong  linen  7  inches  wide,  at  the  head,  and  5 
inches  at  the  tail  of  the  cloth,  to  fasten  it  to  the  reel  by. 
Paste  a  strip  of  linen,  soft  paper,  or  shammy  leather 
(which  is  the  best)  1  §  inch  wide  on  each  rib,  to  keep  the 
cloth  from  fretting.  Then  put  the  cloth  on  the  reel  tight, 
and  sew  or  nail  it  to  the  tail,  and  stretch  it  lengthways  as 
hard  as  it  will  bear,  nailing  it  to  the  head. 

N.  B.  6  yards  of  cloth  covers  a  10  feet  reel. 

Bolting-reels  for  merchant,  are  generally  longer  than 
for  country,  work,  every  part  should  be  stronger  in  pro- 
portion as  necessary.  They  are  best  when  made  to  suit 
the  wide  cloths.  The  socket  gudgeons  at  the  head  should 


334    OF  SETTING  BOLTS  TO  GO  BY  WATER. 

be  much  stronger,  they  being  apt  to  wear  out,  and  trou- 
blesome to  repair. 

The  bolting  hopper  is  made  through  the  floor  above 
the  chest,  IS  inches  square  at  the  upper  and  10  inches 
at  the  lower  end;  the  foremost  side  5  inches  and  the  back 
side  7  inches  from  the  top  of  the  chest. 

The  shoe  2  feet  long  at  the  bottom  of  the  side  pieces, 
slanting:  to  suit  the  hopper  at  the  hinder  end,  set  4  inches 
h'8:her  at  the  Hinder  than  the  fore  end,  the  botto.n  17 
inches  long  and  10  inches  wide.  There  should  be  a  bow 
of  iron  riveted  to  the  fore  end  to  rest  on  the  top  of  the 
knocking  wheel,  fixed  on  the  socket  gudgeon  at  the  head 
of  the  chest,  which  is  10  inches  diameter,  2  inches  thick, 
with  6  half  rounds  cut  out  of  its  circuniference  by  way 
of  knockers,  to  strike  against  the  bow,  and  lift  the  shoe  | 
of  an  inch  every  stroke  to  shake  in  the  meal. 


ART.  29. 

OP  SETTING  BOLTS  TO  GO  BY  WATER. 

The  bolting  reels  are  set  to  go  by  water  as  follows  : 
Make  a  bridge  6  by  4  inches,  and  4  inches  longer  than 
the  distance  of  the  tomkin  posts,  described  art.  20;  set 
it  between  them  on  rests  fastened  into  them,  10  inches 
below  the  cogs  of  the  cog-wheel,  and  the  centre  of  it 
half  the  diameter  of  the  spur-wheel  in  front  of  them;  on 
this  bridge  is  set  the  step  gudgeon,  of  an  upright  shaft, 
with  a  spur-wheel  of  16  or  18  cogs  to  gear  into  the  cog- 
wheel. Fix  a  head-block  to  the  joists  of  the  3d  floor  for 
the  upper  end  of  this  shaft,  put  the  wheel  28,  plate  VII, 
on  it;  hang  another  head-block  to  the  joists  of  the  2d 
floor  near  the  corner  of  the  mill  at  6,  for  the  step  of  the 
short  upright  shaft  that  is  to  be  fixed  there,  to  turn  the 
reels  1  and  9.  Hang  another  head-block  to  the  joists 
of  the  3d  floor  for  the  upper  end  of  the  said  short  up- 
rip^ht,  and  fix  also  head-blocks  for  the  short  shaft  at  the 
head  of  the  reels,  so  that  the  centres  of  all  these  shafts 
will  meet.     Then  fix  a  hanging  post  in  the  corner  5,  for 


OF  MAKING  BOLTING  WHEELS.         53-3; 

'die  gudgeon  of  the  long  horizontal  shaft  27 — 5  to  run  in. 
After  the  head-blocks  are  all  fixed,  then  measure  the 
length  of  each  shaft,  and  make  them  as  follows,  viz. 

The  upright  shaft  5^  inches  for  common  mills,  but 
if  for  merchant-work,  with  Evans's  elevators,  &c.  added, 
make  it  larger  6  or  7  inches ;  the  horizontal  shaft  21 — 5 
and  all  the  other  5  inhes  diameter.  Put  a  socket-gud- 
geon in  the  middle  of  the  long  shafts  to  keep  them  steady; 
make  them  8  or  16  square,  except  at  the  end  where  the 
v\  heels  are  hung,  where  they  must  be  4*  square.  Band 
their  ends,  put  in  the  gudgeons,  put  them  in  their  proper 
places  in  the  head-blocks,  to  mark  where  the  wheels  are 
to  be  put  on  them. 


ART.    30. 

OF  MAKING  BOLTING  WHEELS. 

Make  the  spur-wheel  for  the  first  upright  with  a  4| 
inch  plank,  the  pitch  of  the  cogs  the  same  as  the  cog- 
wheel, into  which  it  is  to  work,  put  two  bands  3-4  of  an 
inch  wide,  one  on  each  side  of  the  cogs,  and  a  rivet  be- 
tween each  cog  to  keep  the  wheel  from  splitting. 

To  proportion  the  cogs  in  the  wheels  to  give  the  bolts 
the  right  motion,  ihe  common  way  is — 

Hang  the  spur-wheel  and  set  the  stones  to  grind  with 
a  proper  motion,  and  count  the  revolutions  of  the  upright 
shaft  in  a  minute,  and  compare  its  revolutions  with  the 
revolutions  that  a  bolt  should  have,  which  is  about  2>&  re- 
volutions in  a  minute.  If  the  upright  goes  1-6  more,  put 
1-6  less  in  the  first  driving-wheel  than  in  the  leader,  sup- 
pose 15  in  the  driver  then  18  in  the  leader:  but  if  their 
difference  be  more  (say  one  half)  there  must  be  a  differ- 
ence in  the  next  two  wheels ;  observing,  that  if  the  mo- 
tion of  the  upright  shaft  be  greater  than  the  bolt  should 
be,  then  the  driving- ^vheel  must  be  proportionably  less 
than  the  leader;  but  if  it  be  slower,  then  the  driver  must 
be  greater  in  proportion.  The  common  size  of  bolting 
wheels  is  from  14  to  20  cogs;  if  less  than  14  the  head- 
blocks  will  be  too  near  the  shafts. 


336  OF  ROLLING-SCREENS. 

Common  bolting  wheels  should  be  made  of  plank  at 
least  3  inches  thick,  well  seasoned,  and  are  best  to  be  as- 
wide  as  the  diameter  of  the  wheel,  and  banded  with  bands 
near  as  wide  as  the  thickness  of  the  wheel,  made  gene- 
rally of  rolled  iron,  about  1-8  of  an  inch  thick.  Some 
make  them  of  two  inch  plank,  crossed,  and  no  bands : 
but  this  proves  no  saving,  as  they  are  apt  to  go  to  pieces 
in  a  few  years.  For  hooping  wheels  see  art.  1 9,  and  for 
finding  the  diameter  of  the  pitch  circle  see  art.  9.  The 
wheels  are  generally  two  inches  more  in  diameter  than 
the  pitch  circle  if  banded;  but  if  not,  they  should  be 
more.  The  pitch  or  distance  of  the  cogs  are  different,  if 
to  turn  1  or  2  bolts  3|  inches,  but  if  more  S| :  but  if 
much  heavy  work,  they  should  not  be  less  than  3  inches. 
Their  cogs  are  half  the  pitch  in  thickness,  the  shank  to 
drive  tight  in  an  inch  auger  hole. 

When  the  mortises  are  made  for  the  shafts  in  the  head, 
and  notches  for  the  keys  to  hang  them,  drive  the  cogs  in 
and  pin  their  shanks  at  the  back  side,  and  cut  them  off 
half  an  inch  from  the  wheel. 

Hang  the  wheels  on  the  shafts  so  that  they  will  gear  a 
proper  depth,  about  2-3  the  thickness  of  the  cogs ;  dress 
all  the  cogs  to  equal  distance  by  a  gauge ;  then  put  the 
shafts  in  their  places,  the  wheels  gearing  properly,  and  the 
head-blocks  all  secure,  set  them  in  motion  by  water. 
Bolting  reals  should  turn  to  drop  the  meal  on  the  back 
side  of  the  chest,  as  it  will  then  hold  more,  and  will  not 
cast  out  the  meal  when  the  door  is  opened. 


ART.    31. 

OF  ROLLING  SCREENS. 

These  are  circular  sieves  moved  by  water,  and  are 
particularly  useful  in  cleaning  wheat  for  merchant  work. 
They  are  of  different  constructions. 

1st.  Those  of  one  coat  of  wire  with  a  screw  in  them. 

2d.  Those  of  two  coats,  the  inner  one  nailed  to  6  ribs, 
the  outer  one  having  a  screw  between  it  and  the  inner 
one. 

3.  Those  of  a  single  coat  and  no  screw. 


OF  FANS.  33^ 

The  first  kind  answers  well  in  some,  but  not  in  all 
eases,  because  they  must  turn  a  certain  number  of  times 
before  the  wheat  can  get  out,  and  the  grain  has  not  so 
good  an  opportunity  of  separating,  there  being  nothing 
to  change  its  position,  it  floats  a  considerable  way  with 
the  same  grains  uppermost. 

The  double  kind  are  better  because  they  may  be  short- 
er and  take  up  less  room ;  and  worse,  for  being  more 
difficult  to  be  kept  clean. 

The  3d  kind  has  this  advantage  ;  we  can  keep  the 
grain  in  it  a  longer  or  shorter  time  at  pleasure,  by  raising 
or  lowering  the  tail  end,  and  is  also  tossed  about  more ; 
but  they  must  be  longer.  They  are  generally  9  or  10 
feet  long,  2  feet  4  inches  diameter,  if  to  clean  for  two  or 
three  pair  of  stones,  but  if  for  more,  they  should  be  lar- 
ger accordingly:  will  clean  for  from  one  to  six  pair  of 
stones.  They  are  made  6  square,  with  6  ribs,  which 
lie  flatwise,  the  outer  corners  taken  off  to  leave  the  edge 
I  of  an  inch  thick ;  the  inner  corners  so  as  to  bring  it 
nearly  to  sharp  edges,  the  wire  work  nailed  on  with  i'i 
ounce  tacks. 

They  are  generally  moved  by  the  same  upright  shaft 
that  moves  the  bolts,  by  a  wheel  on  its  upper  end  with 
two  sets  of  cogs  :  those  that  strike  downwards  gearing 
into  a  wheel  striking  upwards  that  turns  a  laying  shaft, 
with  two  pulleys  on  the  other  end,  one  of  24  inches  dia- 
meter, to  turn  a  fan  with  quick  motion,  the  other  8  inches, 
over  which  passes  a  strap  to  a  pulley  24  inches  diameter, 
on  the  gudgeon  of  the  rolling  screen,  to  reduce  its  mo- 
tion to  about  15  revolutions  in  a  minute.  See  pi.  XIX. 
fig.  23.  This  may  do  for  mills  in  the  small  way,  but 
where  they  are  in  perfection  for  merchant- work,  with 
elevators,  &c.  and  have  to  clean  wheat  for  2,  3,  or  4  pair 
of  stones,  they  should  be  moved  by  cogs. 


ART.    32. 

OF  FANS. 

The  Dutch  fan  is  a  machine  of  great  use  for  blowing 
the  dust  and  other  light  stufi:'  from  among  the  wheat ; 

u  u 


338  OF  THE  SHAKING  SIEVE. 

there  are  various  sorts  of  them ;  those  that  are  only  for 
blowing  the  wheat,  as  it  falls  from  the  rolling-screen,  are 
generally  about  15  inches  long,  and  14  inches  wide  in 
the  wings,  and  have  no  riddle  or  screen  in  them. 

To  give  it  motion,  put  a  pulley  7  inches  diameter  on 
its  axle  for  a  band  to  run  on,  from  the  pulley  on  the  shaft 
that  moves  the  screen  of  24  inches  diameter,  to  give  it  a 
swift  motion;  when  the  band  is  slack  it  slips  a  little  on  the 
small  pulley,  and  the  motion  is  slow  ;  but  vi  hen  tight  the 
motion  is  quicker  ;  by  this  the  blast  is  regulated. 

Some  use  Dutch  fans  complete,  with  riddle  and  screen 
under  the  rolling  screen  for  merchant- work,  and  again 
use  the  fan  alone  for  country-work. 

The  wings  of  those,  which  are  the  common  farmers 
wind- mills  or  fans,  are  18  inches  long,  and  20  inches 
wide,  but  in  mills  they  are  set  in  motion  with  a  pulley 
instead  of  a  cog-wheel  and  wallower. 


ART.    33. 

OP  THE  SHAKING  SIEVE. 

They  are  of  considerable  use  in  country  mills,  to  sift 
indian  meal,  separating  it  into  several  degrees  of  fineness 
if  required,  and  take  the  hulls  out  of  buckwheat  meal, 
that  are  apt  to  cut  the  bolting- cloth,  and  the  dust  out  of 
the  grain,  if  rubbed  before  ground;  and  are  sometimes 
used  to  clean  wheat  or  screenings  instead  of  rolling 
screens. 

If  they  are  for  sifting  meal  they  are  3  feet  6  inches  long, 
9  inches  wide,  3|  inches  deep;  see  it  plate  VI.  fig.  16. 
The  wire-work  is  3  feet  long,  8  inches  wide :  across  the 
bottom  of  the  tail  end  is  a  board  6  inches  wide,  to  the  top 
of  V  hich  the  wire  is  tacked,  and  then  this  board  and  wire 
tacked  to  the  bottom  of  the  frame,  leaving  an  opening  at 
the  tail  end  for  the  bran  to  fall  into  the  box  17,  the  meal 
falling  into  the  meal-trough  15,  the  head-piece  should  be 
strong  to  hold  the  iron  bow  at  15,  through  which  passes 
the  lever  that  shakes  the  sieve,  in  the  following  manner : 
Take  two  pieces  of  hard  wood  15  inches  long,  and  as  wide 


OF  THE  USE  OF  DRAUGHTING  MILLS.     339 

as  the  spindle,  and  so  thick  that  when  one  is  put  on  each 
side  just  above  the  trundle,  it  will  make  it  I^  inch 
thicker  than  the  spindle  is  wide.  The  corners  of  these 
are  taken  off  to  a  half  round,  and  they  are  tied  to  the 
spindle  with  a  small  strong  cord.  These  are  for  to  strike 
against  the  lever  that  works  on  a  pin  near  its  centre, 
which  is  fastened  to  the  sieve,  and  shakes  it  as  the  trun- 
dle goes  round ;  see  it  represented  plate  XVIII.  This 
lever  must  always  be  put  to  the  contrary  side  of  the  spin- 
dle, that  it  is  of  the  meal- spout,  else  it  will  draw  the  meal 
to  the  upper  end  of  the  sieve :  there  must  be  a  spring 
fixed  to  the  sieve  to  draw  it  forward  as  often  as  it  is 
driven  back.  It  must  hang  on  straps  and  be  fixed  so  as 
to  be  easily  set  to  any  descent  required,  oy  means  of  a 
roller  in  form  of  the  feeding  screw,  only  longer,  round 
which  the  strap  w-inds. 

Having  now  given  directions  for  making  and  putting 
to  work,  all  the  machinery  of  one  of  the  completest  of 
the  old  fashioned  gi'ist-mills,  that  may  do  merchant- 
work  in  the  small  way  as  represented  by  plates  XVIII, 
XIX,  XX,  XXI;  but  not  to  near  so  much  advantage  as 
with  the  late  and  new  improvements,  which  are  shown 
by  plate  X. 


ART.    34. 

OP  THE  USE  OF  DRAUGHTING  TO  BUILD  MILLS  BY,  &c. 

Perhaps  some  are  of  opinion  that  draughts  are  useless 
pictures  of  things,  serving  only  to  please  the  fancy.  This 
is  not  what  I  intend  by  them;  but  to  give  the  reader  true 
ideas  of  the  machines,  &c.  described,  or  to  be  made. 
They  are  all  drawn  on  a  small  scale  of  1-8  of  an  inch  for 
a  foot,  in  order  to  suit  the  size  of  the  book,  except  plate 
XVII,  which  is  quarter  of  an  inch  for  a  foot,  and  this 
scale  I  recommend,  as  most  buildings  will  come  on  the 
size  of  a  common  sheet  of  paper. 

N.  B.  Plate  XXIV,  was  made  after  the  above  direc- 
tions, and  has  its  explanations  to  suit  it. 

The  great  use  of  draughting  mills,  &c.  to  build  by,  is 
by  conveying  our  ideas  more  plain,  than  is  possible  to 
be  done  by  writing  or  words,  which  may  be  miscon- 


340  OF  PLANNING  AND  DRAUGHTING  MILLS. 

strued  or  forgotten;  but  a  draught  well  drawn,  speaks 
for  itself,  when  once  understood  by  the  artist;  who,  by 
applying  his  dividers  to  the  draught  and  to  the  scale, 
iinds  the  length,  breadth  and  height  of  the  building,  or 
the  dimensions  of  any  piece  of  timber,  and  its  place  in 
the  building,  &c. 

By  the  draught,  the  bills  of  scantling,  boards,  rafters, 
laths,  shingles,  &c.  &c.  are  known  and  made  out;  it 
should  show  every  wheel,  shaft,  and  machine,  and  their 
places.  By  it  we  can  find  whether  the  house  is  suffi- 
cient to  contain  all  the  works  that  are  necessary  to  carry 
on  the  business ;  the  builder  or  owner  understands  what 
he  is  about,  and  carries  on  cheerfully  without  errof ;  it 
directs  the  mason  where  to  put  the  windows,  doors, 
navel-holes,  the  inner  walls,  &c.  whereas,  if  there  be  no 
draught,  every  thing  goes  on,  as  it  were,  in  the  dark ; 
much  time  is  lost  and  errors  are  committed  to  the  loss 
of  many  pounds.  I  have  heard  a  man  say,  he  believed 
his  mill  was  500/.  better,  by  having  employed  an  expe- 
rienced artist,  to  draw  him  a  draught  to  build  it  by. 
And  I  know  by  experience  the  great  utility  of  them. 
Every  master  builder  ought,  at  least,  to  understand 
them. 


ART.    35. 
DIRECTIONS  FOR  PLANNING  AND  DRAUGHTING  MILLS. 

1st.  If  it  be  a  new  seat,  view  the  ground  where  the 
dam  is  to  be,  and  where  the  mill-house  is  to  stand,  and 
determine  on  the  height  of  the  top  of  the  water  in  the 
head-race  where  it  is  taken  out  of  the  stream ;  and  level 
from  it  for  the  lower  side  of  the  race  down  to  the  seat  of 
the  mill-house,  and  mark  the  level  of  the  water  in  the 
dam  there. 

2d.  Begin  where  the  tail-race  is  to  empty  into  the 
stream,  and  level  from  the  top  of  the  water  up  to  the 
mill-seat,  noticing  the  depth  thereof  in  places  as  you  pass 
along,  which  will  be  of  use  in  digging  it  out. 

Then  find  the  total  fall,  allowing  1  inch  to  a  rod  for  fall 
in  the  races,  but  if  they  are  very  wide  and  long,  less  will  do. 


OF  PLANNING  AND  DRAUGHTING  MILLS  341 

Then,  supposing  the  fall  to  be  21  feet  9  inches,  which 
is  sufficient  for  an  overshot  mill,  and  the  stream  too 
light  for  an  undershot,  consider  well  what  size  stone 
will  suit,  for  I  do  not  recommend  a  large  stone  to  a 
weak,  nor  a  small  one  to  a  strong  stream.  I  have  pro- 
posed stones  4  feet  diameter  for  light,  and  4',6  for  mid- 
dling, and  5  or  5  feet  6  inches  diameter  for  heavy- 
streams.  Suppose  you  determine  on  stones  4  feet,  then 
look  in  table  I,  (which  is  for  stones  of  that  size)  column 
2,  fur  the  fall  that  is  nearest  21  feet  9  inches,  your  fall, 
and  you  find  it  in  the  7tb  example.  Column  3  contains 
the  head  of  water  over  the  wheel  3  feet;  4th,  the  diame- 
ter of  the  wheel  18  feet;  5th,  its  width,  2  feet  2  inches, 
&c.  for  all  the  proportions  to  make  the  stone  revolve  106 
times  in  a  minute. 

Having  determined  on  the  size  of  the  wheels  and  size 
of  the  house,  heights  of  the  stories  to  suit  the  wheels, 
and  machinery  it  is  to  contain,  and  business  to  be  carried 
on  therein,  proceed  to  draw  a  ground  plan  of  the  house, 
such  as  plate  XVIII,  which  is  32  by  55  feet.  See  the 
description  of  tlie  plate.  And  for  the  second  story,  as 
plate  XIX,  &c.  for  the  3d,  4th  and  5th  floors,  if  required, 
taking  care  to  plan  every  thing  for  the  best,  and  so  as 
not  to  clash  one  with  another. 

Draw  an  end  view,  as  plate  XX,  and  a  side  view  as 
plate  XXI.  Take  the  draught  to  the  ground  and  stake 
out  the  seat  of  the  house.  It  is  commonly  best  to  set 
that  corner  of  an  ovefshot  mill  that  the  water  comes  in 
at  farthest  in  the  bank ;  but  take  great  care  to  recon- 
sider and  examine  every  thing  more  than  once  whether 
it  be  planned  for  the  best;  because,  much  labour  is  often 
lost  for  want  of  due  consideration,  and  by  setting  build- 
ings in,  and  laying  foundations  on  wrong  places.  This 
done,  you  may  from  the  draughts  make  out  the  bills  of 
scantling  and  iron  work. 


342  BILLS  OF  SCANTLING. 


ART.    36. 

BILLS  OF  SCANTLING  FOR  A  MILL,  32  BY  55  FEET,  3  STORIES 
HIGH,  SUCH  AS  DESCRIBED  PLA1 ES  XVIII,  XIX,  XX,  AND 
XXI.     THE  WALLS  OF  MASON   WORK. 


For  the  Jirst  Floor, 

5  sills,  S9  feet  long,  8  by  12  inches,  to  lay  on  the  walls 
for  the  joists  to  lay  on. 

48  joists,  10  feet  long,  4  by  9  inches;  all  of  timber  that 
will  last  well  in  damp  places. 

For  the  second  Floor. 
2  posts,  9  feet  long,  IS  by  12  inches. 
2  girders,  30  feet  long,  14  by  16  do. 
48  joists,  10  feet  long,  4-  by  9  do. 

For  the  Floor  over  the  Water-house, 

1  cross  girder,  30  feet  long,  12  by  14  inches,  for  one 
end  of  the  joists  to  lay  on. 

2  posts  to  support  the  girder,  12  feet  long,  12  by  12 
inches. 

16  joists,  13  feet  long,  4  by  9  inches;  all  of  good  white- 
oak  or  other  timber  that  will  last  in  damp  places. 

For  the  third  Floor.  ' 
4  posts,  9  feet  long,  12  by  12  inches,  to  support  the 

girders. 
2  girder-posts,  7  feet  long,  12  by  12  inches,  to  stand  on 

the  water-house. 
2  girders,  53  feet  long,  14  by  16  inches. 
90  joists,  10  feet  long,  4  by  9  inches, 
For  the  fourth  Floor. 

6  posts,  8  feet  long,  10  by  10  inches,  to  support  the 
girders. 

2  girders,  53  feet  long,  13  by  15  inches. 

31)  joists,  10  feet  long,'  4  by  8  do.  for  the  middle  tier  of 
the  floor. 

60  do,  12  feet  do.  4  by  8,  for  the  outside  tiers,  which  ex- 
tends 12  inches  over  the  walls,  for  the  rafters  to  stand 
on. 

2  plates,  54  feet  long,  3  by  10  inches :  these  lay  on  the 
top  of  the  walls,  and  the  joists  on  them. 


BILLS  OF  SCANTLING.  3i^ 

9  raising  pieces,  55  feet  long,  3  by  5  inches ;  these  lay 
on  the  ends  of  the  joists  for  the  rafters  to  stand  on. 

For  the  Roof. 

54  rafters,  22  feet  long,  3  inches  thick,  6|  wide  at  bot- 
tom, and  41  at  top  end. 
2^  collar  beams,  17  feet  long,  3  by  7  inches. 
2760  feet  of  laths,  running  measure. 
7000  shingles. 

For  Doors  and  Window-  Cases. 

12  pieces,  12  feet  long,  6  by  6  inches,  for  door  cases-. 
36  do.  8  feet  long,  5  by  5  inches  for  window-cases. 

For  the  Water-House. 

2  sills,  27  feet  long,  12  by  12  inches. 

1  do.  14  feet  long,  li^  by  12  do. 

2  spur- blocks,  4  feet  6  inches  long  7  by  7  do. 
2  head-blocks,  5  feet  long,  1:3  by  14  do. 

4  posts,  10  feet  long,  8  by  8  to  bear  up  the  penstock. 

2  capsails,  9  feet  long,  8  by  10,  for  the  penstock  to  stand 
on. 

4)  corners  posts,  5  feet  long,  4  by  6  inches,  for  the  cor- 
ners of  the  penstock. 

For  the  Husk  of  a  Mill  of  one  Water-wheel  and  two  Pair 

of  Stones. 

2  sills,  24  feet  long,  12  by  12  inches, 

4  corner  posts,  7  feet  long,  12  by  14  inches. 

2  front  posts,  8  feet  long,  8  by  13  do. 

2  back  posts,  8  feet  do.   10  by  12  inches,  to  support  the 

back  ends  of  the  bridge-trees. 
2  other  back  posts  8  feet  long,  8  by  8  inches. 
2  tomkin  posts,  12  feet  long,  12  by  14  do. 
2  interties,  9  feet  long,  12  by  12  inches,  for  the  outer 

ends  of  the  little  cog-wheel  shafts  to  rest  on. 
2  top  pieces,  10  feet  6  'inches  long,  10  by  10  inches. 
2  beams,  24  feet  long,  16  by  16  inches. 
2  bray-trees,  8^  feet  long,  6  by  12  inches. 
2  bridge-trees,  9  feet  long,  10  by  10  inches. 
4  plank,  8  feet  long,  6  by  1 4  inches,  for  the  stone-bearers. 


344  BILLS  OF  SCANTLING. 

20  plank  9  feet  long,  4  by  about  15  inches,  for  the  tdp  of 
the  husk. 

5  head-blocks,  7  feet  long,  13  by  15  inches,  for  the  wal- 
lower  shafts  to  run  on.  They  serve  as  spurs  also  for 
the  head-block  for  the  water-wheel  shaft. 

For  the  JVater  and  big  Cog-  Wheel. 

1  shaft,  18  feet  long,  S  feet  diameter. 
8  arms  for  the  water-wheel,  18  feet  long,  3  by  9  inches. 
16  shrouds,  %\  feet  long,  2  inches  thick,  and  8  deep. 
16  face  boards,  8  feet  long,  one  inch  thick,  and  9  deep. 
S^  bucket  boards,  2  feet  4j  inches  long,  and  17  inches 

wide. 
140  feet  of  boards,  for  scaling  the  wheel. 

3  arms  for  the  cog-wheel,  9  feet  long,  4  by  14  inches. 
16  cants,  6  feet  long,  4  by  17  inches. 

For  little  Cog-wheels. 

%  shafts  9  feet  long,  14  inches  diameter. 

4  arms,  7  feet  long,  3|  by  10  inches. 
16  cants,  5  feet  long,  4  by  18  inches. 

For  JFalloxvers  and  Trundles. 

60  feet  of  plank,  3|  inches  thick. 

40  feet  do.  3  inches  thick,  for  bolting  gears. 

Cogs  and  Rounds. 

SCO  cogs  to  be  split,  3  by  3,  14  inches  long. 

80  rounds,  do.  3  by  3,  20  inches  long. 

160  cogs,  for  bolting  works,  7  inches  long,  and  1  3-4 
square  :  but  if  they  be  for  a  mill  with  machinery  com- 
plete, there  must  be  more  accordingly. 

Bolting  Shafts. 

1  upright  shaft,  14  feet  long,  5|  by  5|  inches. 

2  horizontal  shafts,  17  feet  long,  5  by  5  inches. 
1  upright  do.  13  feet  long,  5  by  5  inches. 

6  shafts,  10  feet  long,  4  by  4  do. 


BILL  OF  THE  LARGE  IRON,  &c.  345 

ART.   37. 

BILL  OF  THE-  LA^RGE  IROXS   FOR  A  MILL  OF  TWO    PAIR  OP 

*  ,.,j,;..  STONES. 

3  gudgeons,  S" feet  3  inches  long  in  the  shaft;  neck  4| 
inches  long,  3  inches  diameter,  well  steeled  and  turn- 
ed.    See  plate  XII,  fig.  16. 

S  bands,  19  inches  diameter  inside,  |  thick,  and  3  inchei^ 

wide,  for  the  ends  of  the  shaft. 
2  do.  20 i  inches  inside,  h  an  inch  thick,  and  3|  inches 

wide,  for  do. 
2  do.  23  inches  do.  |  an  inch  thick,  and  2|  inches  wide, 

for  do. 

4  gudgeons,  16  inches  in  the  shaft,  3|  inches  long,  and 
2 1  inches  diameter  in  the  neck  for  wallower  shafts  : 
See  fig.  15,  plate  XXIV. 

4  bands,  13  inches  diameter  inside,  1  an  inch  thick,  and 
2  wide,  for  do. 

4  do.  13  inches  do.  ^  an  inch  thick  and  3  wide,  for  do. 

4  wallower  bands,  3  feet  2  inches  diameter  inside,  3 
inches  wide  and  |  of  an  inch  thick. 

4?  trundle  bands,  2  feet  diameter  inside,  3  inches  wide, 
and  I  of  an  inch  thick. 

2  spindles  and  rynes  ;  spindles  5  feet  3  inches  long  from 
the  foot  to  the  top  of  the  necks ;  cock-heads  7  or  8 
inches  long  above  the  necks ;  the  body  of  the  spin- 
dles SI  by  2  inches ;  the  neck  3  inches  long,  and  3 
inches  diameter  :  the  balance  rynes  proportional  to  the 
spindles,  to  suit  the  eye  of  the  stone,  which  is  9  inches 
diameter.     See  plate  XII,  fig.  1,  2,  3. 

2  steps  for  the  spindles,  fig.  4. 

3  sets  of  damsel- irons,  6  knockers  to  each  set. 

3  bray-irons,  3  feet  long,  1 1  inch  wide,  ^  an  inch  thick  '. 
being  a  plain  bar,  one  hole  at  the  lower,  and  6  or  6  at 
the  upper  end. 

JBill  of  Iron  Jor  the  Bolting  a?id  Hoisting-works  in  the 
common  JFay. 

3  spur-wheel  bands,  20  inches  diameter  from  outsides, 
for  the  bolting  spur-wheel,  |  of  an  inch  wide,  and  f 
thick. 

XX 


346  BILL  OF  IRON,  &c. 

2  spur-wheel  bands  12  inches  diameter  from  outsides, 
for  the  hoisting  spur-wheel. 

S  step  gudgeons  and  steps,  10  inches  long,  l-J  inch  thick 
in  the  tang,  or  square  part ;  neck  3  inches  long,  for  the 
upright  shafts.     See  plate  XXIV,  fig.  5  and  6. 

2  bands  for  do.  5  inches  diameter  inside,  1|  wide,  and 
1|  thick. 

2  gudgeons,  9  inches  tang ;  neck  3  inches  long,  11-8 
square,  for  the  top  of  the  uprights. 

8  bands,  4^  inches  diameter  inside. 

1  socket  gudgeon,  1  1-8  of  an  inch  thick  ;  tang  12  inches 
long;  neck  4  inches;  tenon  to  go  into  the  socket  1| 
inch,  with  a  key-hole  at  the  end.     See  fig.  8  and  9. 

14*  gudgeons,  necks  2|  inches,  tangs  8  inches  long,  and 
one  inch  square,  for  small  shafts  and  one  end  of  the 
bolting -reels. 

10  bands  for  do.  4  inches  diameter  inside,  and  1  inch 
wide. 

4  socket-^nidgeons,  for  the  4  bolting-reels,  If  square; 
tangs  8  inches  :  necks  3  inches,  and  tenons  li  inch, 
with  holes  in  the  end  of  the  tangs  for  rivets,  to  keep 
them  from  turning :  the  sockets  1  inch  thick  at  the 
mortise,  and  3  inches  between  the  prongs.     See  fig. 

8  and  9.     Prongs  8  inches  long  and  1  wide. 

8  bandis,  3|  inches,  and  8  do.  4  inches  diameter,  for  the 
bolting-reel  shafts. 

Por  the  Hoisting-wheels. 

2  gudgeons,  for  the  jack- wheel,  neck  31  inches,  and  tang 

9  inches  long,  11-8  square. 

2  bands  for  do.  4|  inches  diameter. 

%  gudgeons,  for  the  hoisting- wheel,  neck  3|  inches,  tang 

9  inches  long,  and  1^  inch  square. 
2  bands,  for  do.  7  inches  diameter. 
6  bands  for  bolting-heads,   16  inches  diameter  inside, 

2|  wide,  and  1-6  of  an  inch  thick. 
6  do.  for  do.  15  inches  do.  do. 

N.  B.  All  the  gudgeons  should  taper  a  little,'  as  the 
sizes  given  are  their  largest  part.  The  bands  for  shafts 
should  be  a  little  widest  at  the  foremost  side  to  make  them 
drive  well ;  but  those  for  heads  should  be  both  sid  es 


EXPLANATION  OF  THE  PLATES.         347 

equal. — 6  picks  for  the  stones,  8  inches  long,  and  1 } 
wide,  will  be  wanted. 


ART.    38.  ^ 

EXPLANATION  OF  THE  PLATES. 

PLATE  XVIL 

Drawn  from  a  scale  of  quarter  of  an  inch  for  a  foot. 
Fig.  1,  a  big  cog-wheel,  8  feet  2  1-3  inches  the  diameter 
of  its  pitch  circle;  8  feet  10  1-3  inches  from  out  to 
out;  69  cogs,  4|  inch  pitch. 

2,  a  little  cog-wheel,  5  feet  10  1-3  inches  the  diameter 
of  its  pitch  circle,  and  6  feet  6  inches  from  out  to  out, 
to  have  52  cogs,  4^  pitch. 

3,  a  wallower,  3  feet  1^  inches  the  diameter  of  its  pitch 
circle,  and  3  feet  4-^  inches  from  out  to  out ;  26  rounds, 
41  pitch. 

4,  a  trundle,  1  foot  8  1-3  inches  the  diameter  of  its  pitch 
circle,  and  1  foot  11  1-3  inches  from  out  to  out;  id 
rounds,  4i  inches  pitch. 

0,  the  back  part  of  the  big  cog-wheel. 

6,  a  model  of  locking  3  arms  together. 

7,  the  plan  of  a  forebay,  showing  the  sills,  caps,  and 
where  the  mortises  are  made  for  the  posts,  with  a  rack 
at  the  upper  end  to  keep  off  the  trash. 

PLATE  XVlll.— The  Ground-plan  of  a  Mill 

Fig.  1  and  8,  bolting-chests  and  reels,  top  view. 

2  and  4,  cog-wheels  that  turn  the  reels. 

3,  cog-wheel  on  the  lower  end  of  a  short  upright  shaft. 

5  and  7,  places  for  the  bran  to  fall  into. 

6,  6,  6,  three  gamers  on  the  lower  floor  for  bran. 

9  and  10,  posts  to  support  the  girders. 

11,  the  lower  door  to  load  wagons,  horses,  &c.  at. 

15,  the  step-ladder,  from  the  lower  floor  to  the  husk. 
13,  the  place  where  the  hoisting  casks  stand  when  fill- 
ing, 

14  and  15,  the  two  meal-troughs  and  meal-spouts. 

16,  meal  shaking  sieve  for  indian  and  buck-wheat. 


34d         EXPLANATION  OF  THE  PLATES. 

Fig.  17,  a  box  for  the  bran  to  fall  into  from  the  sieve. 
18  and  19,  the  head-block,  and  long  spur-block,  for  the 
big  shaft. 

50,  four  posts  in  front  of  the  husks,  called  bray  posts. 

51,  the  water  and  cogwheel  shaft. 

SS,  the  little  cog  wheel  and  shaft,  for  the  lower  stones. 

53,  the  trundle  for  the  burr  stones. 

54,  the  wallower  for  do. 

55,  the  spur-wheel  that  turns  the  bolts. 

56,  the  cog-wheel. 

g7,  the    trundle,    head  wallower    and   bridge-tree,    for 

country  stones. 
Sc,  the  four  back  posts  of  the  husk. - 
S9,  the  two  posts  that  support  the  cross  girder. 

30,  the  two  posts  that  bear  up  the  penstocks  at  one  side. 

31,  the  water-wheel  18  feet  diameter. 

33,  the  two  posts  that  bear  up  the  other  side  of  the 

penstock. 
33,  the  head-blocks  and  spur-blocks,  at  water  end. 
34",  a  sill  to  keep  up  the  outer  ends. 

35,  the  water-house  door. 

36,  a  hole  in  the  wall  for  the  trunk  to  go  through. 

37,  the  four  windows  of  the  lower  story. 

VLATEXlX^Second  Floor, 

Fig  1  and  9,  a  top  view  of  the  bolting-chests  and  reels. 

2  and  10,  places  for  bran  to  fall  into. 

3  and  8,  the  shafts  that  turn  the  reels. 

4  and  7,  wheels  that  turn  the  reels. 

0,  a  wheel  on  the  long  shafts  between  the  uprights. 
6,  a  wheel  on  the  upper  end  of  the  upright  shaft. 
11  and  IS,  two  posts  that  bear  up  the  girders  of  the  third 
floor. 

13,  the  long  shaft  between  two  uprights. 

14,  five  garners  to  hold  toll,  &c. 

15,  a  door  in  the  upper  side  of  the  mill-house. 

16,  a  step-ladder  from  Sd  to  3d  floor. 

17,  the  running  burr  mill-stone  laid  off"  to- be  pressed. 

18,  the  hatchway. 

19,  stair- wa3%  "* 


EXPLANATION  OF  THE  PLATES.         349 

Fig.  SO,  the  running  country  stone  turned  up  to  be 
dressed. 

^1,  a  small  step-ladder  from  the  husk,  to  second  floor. 

S3,  the  places  where  die  cranes  stand. 

24,  the  pulley-wheel  that  turns  the  rolling  screen. 

S5  and  S6,  the  shaft  and  wheel  that  turns  the  rolling- 
screen  and  fan. 

57,  the  wheel  on  the  horizontal  shaft  to  turn  the  bolting- 
reels. 

58,  the  wheel  on  the  upper  end  of  the  first  upright  shaft. 

59,  a  large  pulley  that  turns  the  fan. 

30,  the  pulley  at  the  end  of  the  rolling-screen. 

31,  the  fan.' 

35,  the  rolling-screen. 

33,  a  step-ladder  from  the  husk  to  the  floor  over  the 

water-house. 
34?  and  35,  two  posts  that  support  the  girders  of  the  3d 

floor. 

36,  a  small  room  for  the  tailings  of  the  rolling-screen, 

37,  a  room  for  the  fannings. 

38,  do.  for  the  screenings. 

39,  a  small  room  for  the  dust. 

40,  the  penstock  of  water. 

41,  a  room  for  the  miller  to  keep  his  books  in. 
4rS,  a  fire-place. 

43,  the  upper  end  door. 

44,  ten  windows  in  the  Sd  story,  IS  lights  each. 

PLATE  XX. 

Represents  a  view  of  the  lower  side  of  a  stone  mill-house 
.  three  stories  high,  which  plan  will  suit  tolerably  well  for  a 
two  story  house,  if  the  third  story  be  not  wanted.  Part 
of  the  wall  supposed  to  be  open,  so  that  we  have  a  view 
of  the  stones,  running  gears,  &c. 

Line  1  represents  the  lower  floor,  and  is  nearly  level 
M'ith  the  top  of  the  sills,  of  the  husk  and  water-house. 
S,  3  and  4  the  second,  third,  and  fourth  floors. 
5  and  6  are  windows  for  admitting  air  under  the  lower 

floor. 
7  the  lower  door,  with  steps  to  ascend  to  it,  which  com- 
monly suits  best  to  load  from. 


350         EXPLANATION  OF  THE  PLATES. 

8  the  arch  over  the  tail-race  for  the  water  to  run  from 
the  wheel. 

9  the  water-house  door,  which  sometimes  suits  better 
to  be  at  the  end  of  the  house,  where  it  makes  room  to 
wedge  the  gudgeon. 

10  the  end  of  the  water-wheel  shaft. 

11  the  big  cog-wheel  shaft. 

12  the  little  cog-wheel  and  wallower,  the  trundle  being 
seen  through  the  window. 

13  the  stones  with  the  hopper,  shoe  and  feeder,  as  fixed 
for  grinding. 

14  the  meal-trough. 

We  have  an  end  view  of  the  husk  frame- — there  are 
thirteen  windows  with  twelve  lights  each. 

PLATE  XXL 

Represents  an  outside  view  of  the  water  end  of  a  mill- 
house,  and  is  to  show  the  builders,  both  masons,  car- 
penters and  mill-wrights,  the  height  of  the  walls,  floors, 
and  timbers ;  places  of  the  doors  and  windows,  with  a 
view  of  the  position  of  the  stones  and  husk-timbers,  sup- 
posing the  wall  open  so  that  we  could  see  them. 
Fig.  1,  3,  3,  and  4  shows  the  joists  of  the  floors. 

5  represents  a  fish  turning  with  the  wind  on  an  iron  rod, 
which  does  as  well  as  a  weather-cock. 

6  the  end  of  the  shaft  for  hoisting  outside  of  the  house, 
which  is  fixed  above  the  collar-beams  above  the 
doors,  to  suit  to  hoist  into  either  of  them,  or  either 
story,  at  either  end  of  the  house,  as  may  best  suit. 

7  the  dark  squares,  showing  the  ends  of  the  girders. 

8  the  joists  over  the  water-house.  ^ 

9  the  mill- stones,  with  the  spindles  they  run  on,  and  the 
ends  of  the  bridge- trees  as  they  rest  on  the  brays  a  a. 
b  b  shows  the  end  of  the  brays,  that  are  raised  and 
lowered  by  the  levers  c  c,  called  the  lighter-staflfs, 
thereby  raising  and  lowering  the  running  stone. 

10  the  water-wheel  and  big  cog-wheel. 

11  the  wall  between  the  water  and  cog-wheel. 
IS  the  end  view  of  the  two  side  walls  of  the  house. 

Plate  X  is  explained  in  the  Preface. 


OF  SAW-MILLS.  351 

ART.   39. 

OP  SAW  MILLS— THEIR  UTILITY. 

They  are  for  sawing  timber  into  all  kinds  of  scantling, 
boards,  laths,  &c.  &c.  are  used  to  great  advantage  where 
labour  is  dear.  One  mill,  attended  by  one  man,  if  in 
good  order,  will  saw  more  than  30  men  will  with  whip- 
saws,  and  much  more  exactly. 

Construction  of  their  Water-wheels. 

They  have  been  variously  constructed  ;  the  most  sim- 
ple and  useful  of  which,  where  water  is  plenty,  and  above 
six  feet  fall,  is  the  flutter-wheel ;  but  where  water  is 
scarce  in  some  cases,  and  for  want  of  sufficient  head  in 
others,  to  give  flutter-wheels  sufficient  motion,  high 
wheels,  double  geared,  have  been  found  necessary. 
Flutter- wheels  may  be  made  suitable  for  any  head  above 
six  feet,  by  making  them  low  and  wide,  for  low  heads  ; 
and  high  and  narrow  for  high  ones,  so  as  to  make  about 
120  revolutions,  or  strokes  of  the  saw,  in  a  minute  : 
but  rather  than  double  gear  I  would  be  satisfied  with 
100. 


352 


OF  SAW  MILLS. 


A  TABLE 


DIAMETER  OF  FLUTTER  WHEELS, 

Prom  out  to  outsides,  and  their  width  in  the  clear,  stiitable  to  all  heads, 
from  6  to  30  feet. 


n 
o 

3 
n 

J? 

ft. 

ft.  in. 

ft. in. 

6 

2:8 

5:6 

7 

2:10 

5:0 

8 

2:11 

4:8 

9 

3:0 

4:3 

10 

3:1 

4:0 

11 

3:2 

3:9 

12 

3:3 

3:6 

13 

3:4 

•  3:3 

14 

3:5 

3:0 

15 

3:6 

2:9 

16 

3:7 

2:6 

17 

3:8 

2:4 

18 

3:9 

2:2 

19 

3:10 

2:0 

20 

3:11 

1:10 

21 

4:0 

1:9 

22 

4:1 

1:8 

23 

4:2 

1:7 

24 

4:3 

1:6 

25 

4:4 

1:5 

26 

4:5 

1:4    « 

27 

4:6 

1:3 

28 

4:7 

1:2 

29 

4:8 

1:1 

30 

4:9 

1:0 

N.  B.  The  above  wheels  are  proposed  as  narrow  as 
will  well  do  on  account  of  saving  water  ;  but  if  there  is 
very  plenty  of  it,  the  wheels  may  be  made  wider  than 
directed  in  the  table,  and  the  mill  will  be  more  pow- 
erful. 


OF  SAW-MILLS.  S5t 


Of  Gearing  Saw-Mills, 

Of  this  I  shall  say  but  little,  they  being  expensive  and 
but  little  used. — They  should  be  geared  so  as  to  give  the 
saw  about  120  strokes  in  a  minute,  when  at  work  in  a 
common  log.  The  water-wheel  is  like  that  of  another 
mill,  whether  of  the  undershot,  overshot,  or  breast  kind  ; 
the  cog-wheel  of  the  spur  kind,  and  as  large  as  will  clear 
the  water.  The  wallower  commonly  has  14  or  15 
rounds,  but  so  as  to  produce  the  right  motion.  On  the 
wallower  shaft  is  a  balance- n^heel,  which  may  be  of  stone 
or  wood :  this  is  to  regulate  the  motion.  There  should 
be  a  good  head  above  the  water-wheel  to  give  it  a  lively 
motion,  else  the  mill  will  run  heavily. 

The  mechanism  of  a  complete  saw-mill  is  such  as  to 
produce  the  following  effects,  viz. 

1.  To  move  the  saw  up  and  down,  with  a  sufficient 
motion  and  power. 

2.  To  move  the  log  to  meet  the  saw. 

3.  To  stop  of  itself  when  within  3  inches  of  being 
through  the  log. 

4.  To  draw  the  carriage  with  the  log  back  by  the 
power  of  water  ready  to  enter  again. 

The  mill  is  stopped  as  follows,  viz.  When  the  gate 
is  drawn  the  lever  is  held  by  a  catch,  and  there  is  a  trig- 
ger, one  end  of  which  is  within  half  an  inch  of  the  side 
of  the  carriage,  on  which  is  a  piece  of  wood  an  inch  and 
a  half  thick,  nailed  so  that  it  will  catch  against  the  trig- 
ger as  the  carriage  moves,  which  throws  the  catch  off 
of  the  lever  of  the  gate,  and  it  shuts  down  at  a  prop«r 
time. 


Description  of  a  Saw-mill. 

Plate  XXIllis  an  elevation  and  perspective  view  of  a 
saw-mill,  showing  the  foundation,  walls,  frame,  &c.  &c. 

Fig.  0.  1.  the  frame  uncovered,  52  feet  long,  and  12 
feet  wide. 

Fig  2.  the  lever  for  communicating  the  motion  from 
the  saw-gate  to  the  carriage,  to  move  the  log.  It  is  8  feet 
long,  3  inches  square,  tenoned  into  a  roller  6   inches 

Y  ^- 


854  OF  SAW-MILLS. 

diameter,  reaching  from  plate  to  plate,  and  working  on 
gudgeons  in  them ;  in  its  lower  side  is  framed  a  block  10 
inches  long,  with  a  mortise  in  it  S  inches  wide,  its  whole 
length,  to  receive  the  upper  end  of  the  hand-pole,  having 
in  it  ?5everal  holes  for  an  iron  pin,  to  join  the  hand-pole  to 
it  to  regulate  the  feed,  by  setting  the  hand-pole  nearer 
the  centre  of  the  roller  to  give  less,  and  farther  off,  to 
give  more  feed. 

Fig.  3.  the  hand-pole  or  feeder,  12  feet  long,  and  3 
inches  square  where  it  joins  the  block. 

Fig.  4.  tapering  to  2  inches  at  the  lower  end,  on  which 
is  the  iron  hand  1  foot  long,  with  a  socket,  the  end  of 
which  is  flattened,  steeled  and  hardened,  and  turned 
down  at  each  side  half  an  inch,  to  keep  it  on  the  rag- 
wheel. 

Fig.  5.  the  rag  wheel.  This  has  four  cants  4f  feet 
long,  17  by  3  inches  in  the  middle,  lapped  together  to 
make  the  wheel  5  feet  diameter,  is  faced  between  the 
arms  with  2  inch  plank  to  strengthen  the  laps.  The 
cramp  or  ratchet-iron  is  put  on  as  a  hoop  near  1  inch 
square,  with  ratchet-notches  cut  on  its  outer  edge,  about 
3  to  an  inch.  On  one  side  of  the  wheel  are  put  12  strong 
pins,  nine  inches  long,  to  tread  the  carriage  back,  when 
the  backing  works  are  out  of  order.  On  the  other  side 
are  the  cogs,  about  56  in  number,  3  inch  pitch  to  gear 
into  the  cog-vrheel  on  the  top  of  the  tub-wheel  shaft,  with 
15  or  16  cogs.  In  the  shaft  of  the  rag-wheel  are  6  or  > 
rounds,  1 1  inches  long  in  the  round  part,  let  in  near  their 
whole  thickness,  so  as  to  be  of  a  pitch  equal  to  the  pitch 
of  the  cogs  of  the  carriage,  and  gear  into  them  easily  :  the 
ends  are  taperetl  off  outside,  and  a  bund  drove  on  tliem  at 
each  end,  to  keep  them  in  their  places. 

Fig.  6.  the  carnage.  Is  a  frame  4  feet  W'ide  from  out- 
sides,  one  side  29  feet  long,  7  by  7  inches ;  the  other  32 
feet  long,  8  by  7  inches,  very  straight  and  true,  the  inter- 
ties  at  each  end  15  by  4  inches,  strongly  tenoned  and 
braced  into  the  sides  to  keep  the  frame  from  racking. 
In  the  under  side  of  the  largest  piece  are  set  two  rows  of 
cogs,  2  inches  between  the  rows,  and  9  inches  from  the 
fore  side  of  one  cog  to  that  of  another  :  the  cogs  of  one 


OF  SAW-MILLS.  355 

row  between  those  of  the  other,  so  as  to  make  4|  Inch 
pitch,  to  gear  into  the  rounds  of  the  rag-wheel.  The 
cou^s  are  about  60  in  number ;  shank  7  inches  long,  1 
3  4f  inch  square  ;  head  2  3-4!  long,  2  inches  thick  at  the 
points,  and  2^  inches  at  the  shoulder. 

Fig.  7.  the  ways  for  the  carriage  to  run  on.  These  are 
strips  of  plank  4|  inches  wide,  2  inches  thick,  set  on 
edge,  let  1|  inch  into  the  top  of  the  cross  sills,  of  the 
whole  length  of  the  mill,  keyed  fast  on  one  side,  made 
very  straight  both  side  and  edge,  so  that  one  of  them  will 
pass  easily  between  the  rows  of  cogs  in  the  carriage,  and 
leave  no  room  for  it  to  move  sideways.  They  should  be 
of  hard  wood,  well  seasoned,  and  hollowed  out  between 
the  sills  to  keep  the  dust  from  lodging  on  them. 

Fig.  8.  the  fender  posts.  The  gate  with  the  saw  plays 
in  rabbets  2|  deep  and  4  inches  wide,  in  the  fender 
posts,  which  are  13  feet  long,  and  12  inches  square,  hung 
by  hooked  tenons,  the  front  side  of  the  two  large  cross 
beams  in  the  middle  of  the  frame,  in  mortises  in  their  up- 
per sides,  so  that  they  can  be  moved  by  keys  to  set  them 
plumb.  There  are  3  mortises  two  inches  square  through 
each  post,  within  half  an  inch  of  the  rabbets,  through 
which  pass  hooks  with  large  heads,  to  keep  the  frame  in 
the  rabbets  :  they  are  keyed  at  the  back  of  the  posts. 

Fig.  9.  the  saw,  which  is  6  feet  long,  7  or  8  inches 
wide  when  nevy,  hung  in  a  frame  6  feet  wide  from  the 
outsides,  6  feet  3  inches  long  between  the  end  pieces,  the 
lowermost  of  which  is  14  by  S  inches,  the  upper  one  12 
by  3,  the  side  pieces  5  by  3  inches,  10  feet  long,  all  of 
the  best  dry,  hard  wood.  The  saw  is  fastened  in  the 
frame  by  two  irons  in  form  of  staples,  the  lo\ver  one  with 
two  screw  pins  passing  through  the  lower  end,  screw- 
ing one  leg  to  each  side  of  the  end  piece  :  the  legs  of 
the  upper  one  are  made  into  screws,  one  at  each  side  of 
the  end  piece,  passing  through  a  broad  flat  bar  that  rests 
on  the  top  of  the  end  piece,  with  strong  burrs  1  3-4  inch 
square,  to  be  turned  by  an  iron  span  made  to  fit  them. 

These  straps  are  made  of  flat  bars,  3  feet  9  inches  long, 
3  inches  wide,  3-4  thick  before  turned  ;  at  the  turn  they 
are  5  inches  wide,  square,  and  split,  to  receive  the  saw, 


356  OF  SAW-MILLS. 

and  tug-pins,  then  brought  nearer  together,  so  as  to  fit 
the  gate.  The  saw  is  stretched  tight  in  this  frame,  by 
the  screws  at  the  top,  exactly  in  the  middle  at  each  end, 
measuring  from  the  outside  ;  the  top  end  standing  about 
half  an  inch  more  forward  than  the  bottom. 

Fig.  10.  the  forebay  of  water  projecting  through  the 
upper  foundation  wall. 

Fig.  11.  the  flutter- wheel.  Its  diameter  and  length  ac- 
cording; to  the  head  of  water,  as  shown  in  the  table.  The 
floats  i.re  fastened  in  with  keys,  so  that  they  will  drive 
inward,  when  any  thing  gets  under  them,  and  not  break. 
These  wheels  should  be  very  heavy,  that  they  may  act 
as  a  fly  or  balance  to  regulate  the  motion,  and  work  more 
powerfully. 

Fig.  13.  the  crank — see  it  represented  by  a  draught 
from  a  scale  of  1  foot  to  an  inch — pi.  XXIV.  fig.  17. 
The  part  in  the  shaft  2  feet  3  inches  long,  3|  by  2  inches, 
neck  8  inches  long  3  thick,  and  12  inches  from  the  centre 
of  the  neck  to  the  centre  of  the  wrist  or  handle,  which  is 
5  inches  long  to  the  key  hole,  and  2  inches  thick. 

The  gudgeon  at  the  other  end  of  the  shaft  is  18  inches - 
in  the  shaft,  neck  35  long,  2|  diameter. 

The  crank  is  fastened  in  the  same  way  as  gudgeons. 
See  art.  13. 

Fig.  12 — 13.  the  pitman  ;  which  is  Si  inches  square 
at  the  upper  end,  4i  in  the  middle,  and  4  near  the  lower 
end  ;  but  20  inches  of  the  lower  end  is  4i  by  5^,  to  hold 
the  boxes  and  key,  to  keep  the  handle  of  the  crank 
tight. 

Pitman  Irons  of  an  improved  Construction. 

See  plate  XXIV.  fig.  10,  11,  12,  13,  14.  18.  Fig.  10. 
is  a  plate  or  bar,  with  a  hole  in  each  end,  through  which 
the  upper  ends  of  the  lug-pins  11 — 11  pass,  with  a  strong 
burr  screwed  on  each,  they  are  17  inches  long,  11-8 
inch  square,  turned  at  the  lower  end  to  make  a  round 
hole  11-8  diameter,  made  strong  round  the  hole. 

t\g.  i2.  is  a  large  flat  link,  through  a  mortise  near  the 
lower  side  of  the  end  of  the  saAv-frame.     The  lug-pins 


OF  SAW-MILLS.  357 

pass  one  through  each  end  of  this  link,  which  keeps 
them  close  to  the  gate  sides. 

Fig.  14  is  a  bar  of  iron  2  feet  long,  3|  inches  wide,  i 
inch  thick,  at  the  lower  end,  and  1  1-8  at  the  upper  end. 
It  is  split  at  the  top  and  turned  as  the  fig.  to  pa.ss  through 
the  lug-pins.  At  fig.  13  there  is  a  notch  set  in  the  head 
of  the  pitman  bar  14,  1  i  inch  long,  nearly  as  deep  as  to 
be  in  a  straight  line  with  the  lower  side  of  the  side  pins 
made  a  little  hollow,  steeled  and  made  very  hard. 

Fig.  18  is  an  iron  plate  ii  inch  wide,  half  an  inch 
thick  in  the  middle,  with  2  large  nail-holes  in  each  end, 
and  a  round  piece  of  steel  welded  across  the  middle  and 
hardened,  made  to  fit  the  notch  in  the  upper  end  of  the 
pitman,  pi.  XXVI.  and  draw  close  by  the  lug-pins,  to  the 
underside  of  the  saw-frame  and  nailed  fast.  Now,  if  the 
bearing  part  of  this  joint  be  in  a  straight  line,  the  lower 
end  of  the  pitman  may  play  without  friction  in  the  joint, 
because  both  the  upper  and  lower  parts  will  roll  without 
sliding,  like  the  centre  of  a  scale  beam,  and  will  not  wear. 
This  is  by  far  the  best  plan  for  pitman  irons.  The  first 
set  I  ever  seen  or  heard  of  has  been  in  my  saw-mill  8 
years,  doing  much  hard  work,  and  has  not  cost  three 
minutes  to  adjust  them ;  whereas  others  are  frequently 
very  troublesome. 

Fig.  l-i,  the  tub-wheel  for  running  the  carriage  back. 
This  is  a  very  light  whe«l,  4  feet  diameter,  and  put  in 
motion  by  a  motion  of  the  foot  or  hand,  at  once  throw- 
ing it  in  gear  with  the  rag-wheel,  lifting  off  the  hand  and 
clicks  from  the  ratchet,  and  hoisting  a  little  gate  to  let 
water  on  the  wheel.  The  moment  the  saw  stops,  the 
carriage  with  the  log  begins  to  move  gently  back  again. 
Fig.  15,  the  cog-wheel  on  the  top  of  the  tub- wheel 
shaft,  with  15  or  16  cogs. 

Fig.  16,  the  log  on  the  carriage,  sawed  part  through. 
Fig.  17,  a  crank  and  windlas  to  increase  power,  by 
which  one  man  can  draw  heavy  logs  on  the  mill,  and 
turn  them  by  a  rope  round  the  log  and  windlas. 
Fig.  18,  a  cant  hook  for  rolling  logs. 
Fig.   19,  a  double  dog,  fixed  into  the  hindmost  head- 
block,  used  by  some  to  hold  the  log. 

Fig.  20,  are  smaller  dogs  to  use  occasionally  at  either 
end. 


358  OF  A  FULLING-MILL. 

Fig.  21 — 22,  represents  the  manner  of  shuting  water 
on  a  flutter-wheel  by  a  long  open  shute,  which  should 
not  be  more  perpendicular  than  an  angle  of  45  degrees, 
lest  the  water  should  rise  from  the  shute  and  take  air,, 
which  VA  ould  be  a  great  loss  of  power. 

Fig.  2S,  represents  a  long,  perpendicular,  tight  shute  ; 
the  gate  33  is  always  drawn  fully,  and  the  quantity  of 
water  regulated  at  the  bottom  by  a  little  gate  r  for  the 
purpose.  There  must  be  air  let  into  this  shute  by  a  tube 
entering  at  a.*  These  shutes  are  for  saving  expense 
where  the  head  is  great,  and  should  be  much  larger  at 
the  upper  than  lower  end,  else  there  will  be  a  loss  of 
power.f  The  perpendicular  ones  suit  best  where  a  race 
passes  within  12  feet  of  the  upper  side  of  the  mill. 

OPERATION. 

The  sluice  drawn  from  the  penstock  10,  puts  the 
wheel  11  in  motion — the  crank  13  moves  the  saw-gate 
and  saw  9  up  and  down,  and  as  they  r^se  they  lift  up  the 
lever  2,  which  pushes  forward  the  hand-pole  3,  which 
moves  the  rag-wheel  5,  which  gears  in  the  cogs  of  the 
carriage  6,  and  ,draws  forward  the  log  16  to  meet  the 
saw,  as  much  as  is  proper  to  cut  at  a  stroke.  When  it 
is  within  3  inches  of  being  through  the  log,  the  cleet  C, 
on  the  side  of  the  carriage,  arrives  at  a  trigger  and  lets  it 
fly,  and  the  sluice-gate  shuts  down  ;  the  miller  instantly 
draws  water  on  the  wheel  14,  which  runs  the  log  gently 
back,  &c.  &c. 


ART.    40. 

i 
DESCRIPTION  OF  A   FULLING-MILL. 

Fig.  19,  plate  XXIV,  is  the  penstock,  water-gate  and 
spout  of  an  overshot  fulling-mill,  the  whole  laid  down 
from  a  scale  of  4  feet  to  an  inch. 

Fis;.  20,  one  of  the  3  interties,  that  are  framed  one  end 
into  the  front  side  of  the  top  of  the  stock-block ;  the 
other  ends  into  the  tops  of  the  3  circular  pieces  that 

•  The  use  of  this  air-tiibe  is  shown  art.  71,  page  161. 
I  Must  be.  very  strong  else  they  will  burst. 


OF  A  FULLING-MILL.  359 

guide  the  mallets ;  they  are  G  feet  long,  5  inches  wide, 
and  6  deep. 

Fig.  SI  are  the  two  mallets;  they  are  4"  feet  3  inches 
long,  21  inches  wide,  and  8  thick,  shaped  as  in  the 
figure. 

Fi^.  22  their  handles,  8  feet  long,  20  inches  wide,  and 
3  thick.  There  is  a  roller  passes  through  them,  8  inches 
from  the  upper  ends,  and  hang  in  the  hindermost  corner 
of  the  stock-post.  The  other  ends  go  through  the  mal- 
lets, and  have  each  on  their  underside  a  plate  of  iron 
faced  with  steel  and  hardened,  2  feet  long,  3  inches 
wide,  fastened  by  screw-bolts,  for  the  tappet-blocks  to 
rub  against  while  lifting  the  mallets. 

Fig.  23  the  stock-post,  7  feet  long,  2  feet  square  at 
the  bottom,  15  inches  thick  at  top,  and  shaped  as  in  the 
figure. 

Fig.  24-  the  stock  where  the  cloth  is  beaten,  shaped 
inside  as  in  the  figure,  planked  inside  as  high  as  the 
dotted  line,  which  planks  are  put  in  rabbets  in  the  post^ 
the  inside  of  the  stock  being  18  inches  wide  at  bottom, 
1 9  at  top,  and  2  feet  deep. 

Fig.  25  one  of  the  3  circular  guides  for  the  mallets ; 
they  are  6  feet  long,  7  inches  deep,  and  5  thick;  are 
framed  into  a  cross  sill  at  bottom  that  joins  its  lower 
edge  to  the  stock-post.  This  sill  forms  part  of  the  bot- 
tom of  the  stock,  and  is  4  feet  long,  20  inches  wide,  and 
10  thick. 

The  sill  under  the  stock-post  is  6  feet  long,  20  inches 
wide,  and  18  thick.  The  sill  before  the  stock  is  6  feet 
long,  and  14  inches  square. 

Fig.  26  the  tappet-arms,  5  feet  6  inches  long,  21 
inches  each  side  the  shaft,  12  inches  wide,  and  4  thick. 
Therh  is  a  mortise  through  each  of  them  4  inches  wide, 
the  length  from  shaft  to  tappet,  for  the  ends  of  the  mal- 
let handles  to  pass  through.  The  tappets  are  4  pieces 
of  hard  wood,  12  inches  long,  5  wide,  and  4  thick, 
made  in  the  form  of  half  circles  pinned  to  the  ends  of 
the  arms. 

Fig.  27  the  overshot  water-wheel,  similar  to  other  mills. 

Fig.  28  one  of  the  3  sills,  16  feet  long,  and  12  inches 
square,  with  w  alls  under  them  as  in  the  figure. 


360  OF  A  FULLING-MILL,  &c. 

OPERATION. 

The  cloth  is  put  in  a  loose  heap  into  the  stock  24; 
the  water  being  drawn  on  the  wheel,  the  tappet-arms  lift 
the  mallets  alternately,  which  strike  the  under  part  of 
the  heap  of  cloth,  and  the  upper  part  is  continually  fall- 
ing over,  and  thereby  turning  and  changing  its  position 
under  the  mallets,  which  are  of  the  shape  in  the  figure, 
to  produce  this  effect. 

Description  oftheDrawings  of  the  Iron-work  s^PlateXXlV, 

Fig.  1  is  a  spindle,  2  the  balance-ryne,  and  3  the  dri- 
ver, for  a  mill-stone.  The  length  of  the  spindle  from 
the  foot  to  the  top  of  the  neck  is  about  5  feet  3  inches ; 
cock-head  8  or  9  inches  from  the  top  of  the  neck,  which 
is  3  inches  long,  and  3  diameter;  blade  or  body  3|  by 
2  inches;  foot  1|  inch  diameter;  the  neck,  foot,  and  top 
of  the  cock-head,  steeled,  turned  and  hardened. 

Fig.  %  the  balance-ryne,  is  sometimes  made  with  3 
horns,  one  of  which  is  so  short  as  only  to  reach  to  the 
top  of  the  driver,  which  is  let  into  the  stone  right  under 
it ;  the  other  to  reach  near  as  low  as  the  bottom  of  the 
driver :  but  of  late  are  mostly  made  with  2  horns  only, 
which  may  be  made  sufficiently  fast  by  making  it  a  little 
wider  than  the  eye,  and  let  into  the  stone  a  little  on  each 
side  to  keep  it  steady  and  from  moving  sideways.  Some 
choose  them  with  four  horns,  which  fills  the  eye  too 
much. 

Fig.  3  is  a  driver,  about  15  inches  long. 

Fig  4  the  step  for  the  spindle  foot  to  run  in.  It  is  a 
box  6  inches  long,  4  inches  wide  at  top,  but  less  at  bot- 
tom, and  4  inches  deep  outsides,  the  sides  and  bottom 
half  an  inch  thick.  A  piece  of  iron  1  inch  thick  is  fitted 
to  lay  tight  in  the  bottom  of  this  box,  but  not  welded ; 
in  the  midle  of  which  is  welded  a  plug  of  steel  1  \  inch 
square,  in  which  is  punched  a  hole  to  fit  the  spindle-foot 
a  quarter  af  an  inch  deep.  The  box  must  be  tight  to 
hold  oil. 

Fig.  5  a  step-gudgeon  for  large  upright  shafts,  16  inches 
long  and  two  square,  steeled  and  turned  at  the  toe. 

Fig.  6  the  step  for  it,  similar  to  4  but  less  proportion- 
able. 


OF  SAW- MILLS.  36t 

Fig.  7  is  a  gudgeon  for  large  bolting- shafts,  13  inches 
long  and  1|  square. 

Fig.  8  a  large  joint-gudgeon,  tang  14  inches,  neck  5, 
and  tenon  2  inches  long,  1|  square. 

Fig.  9  the  socket  part  to  fit  the  shaft,  with  3  rivet<s 
holes  in  each. 

Fig.  10 — 14 — 18  pitman- irons,  described  art.  39. 

Fig.  15  the  wallo\ver  gudgeon,  tang  16  inches,  neck 
3 1  inches  long,  and  2-^  diameter. 

Fig.  16  the  water-wheel  gudgeon,  tang  3  feet  2  inches 
long,  neck  4-^  inches  ditto,  3|  square. 

tig.  17  a  saw-mill  crank,  described  art.  39. 

N.  B  The  spindle-ryne,  &c.  is  drawn  from  a  scale  of 
2  feet  to  an  inch,  and  all  the  other  irons  1  foot  to  an  inch. 


In  addition  to  what  is  said  of  Saw-mills,  by  Tho- 
mas Ellicott,  I  add  the  following. 

Of  hanging  the  Saw. 

First,  set  the  fender  posts  as  near  plumb  every  way  as  possible,  and  the 
head-blocks  on  which  the  log-  is  to  lay,  level.  Put  the  saw  right  in  he 
middle  of  the  gate,  me^isuring  from  the  out  sides,  with  the  upper  teeth 
about  half  an  inch  farther  forward  than  the  lower  ones;  set  it  by  the  gate 
and  not  by  a  plumb  line — this  is  to  give  the  saw  liberty  to  rise  without 
cutting,  and  the  log  room  to  push  forward  as  it  rises.  Run  the  carriage 
forward,  so  that  the  saw  strike  the  block — stick  up  a  nail,  &c.  there — run 
it  back  again  its  full  length,  and  standing  behind  the  saw,  set  it  to  direct 
exactly  to  the  mark.  S'retch  the  saw  in  the  frame,  rather  most  at  the 
edge,  that  it  may  be  stifTest  there.  Set  it  to  go,  and  hold  a  tool  close  to 
one  side,  and  observe  whether  it  touch  equally  the  whole  length  of  the 
stroke — try  if  it  be  square  with  the  top  of  the  head  blocks,  else  it  will  not 
make  the  scantling  square. 

Of  xvhetting  the  Saw. 

The  edge  of  the  teeth  ought  to  be  kept  straight,  and  not  suffered  to 
wear  hollowing — the  teeth  seta  little  out,  equal  at  each  side,  and  the  outer 
corners  a  little  longest— they  will  clear  their  way  the  better.  Some  whet 
the  under  side  of  the  teeth  nearly  level,  and  others  a  little  droopmg  down ; 
but  then  it  will  never  saw  steady — will  be  apt  to  wood  too  much  ;  they 
should  slope  a  little  up,  but  very  little,  to  make  it  work  steady.  Try  a 
cut  through  the  log,  and  if  it  comes  out  at  the  mark  made  to  set  it  by,  it  is 
shown  to  be  right  hung- 

Z  Z 


362  OF  SAW-MILLS. 


Of  springing  Logs  straight. 

Some  long  small  logs  will  spring  so  much  in  sawing  as  to  spoil  the 
scantling,  unless  they  can  be  held  straight  :  to  do  which  make  a  clamp  to 
bear  with  one  end  against  the  side  of  the  carriage,  the  other  end  under  the 
log  with  a  post  up  the  side  thereof — drive  a  wedge  between  the  post  and 
log.  and  spring  it  straight;  this  will  bend  the  carriage  side — but  this  is  no 
injury. 

Of  moving  the  Logs,  to  the  Size  of  the  Scantling,  i^c. 

Make  a  sliding-block  to  slide  in  a  rabbet  in  front  of  the  main  head  block; 
fasten  the  log  to  this  with  a  little  dog  on  each  side,  one  end  of  which  being 
round,  is  drove  into  around  hole,  in  the  front  side  of  the  sliding-block,  the 
other  flatted  to  drive  in  the  log,  cutting  across  the  grain,  slanting  a  little 
out — it  will  draw  the  log  tight,  and  stick  in  the  better.  Set  a  post  ot  hard 
wood  in  the  middle  of  the  main  block  close  to  the  sliding  one,  and  to  ex- 
tend with  a  shoiilder  over  tht-  slidintj  one,  for  a  wedge  to  be  drove  under 
this  shoulder  to  keep  the  block  light.  Make  a  mark  on  each  block  to 
measure  from — when  the  log  is  moved  thf  key  is  driven  out.  The  other 
end  next  the  saw  is  best  held  by  a  sliding  dog,  part  on  each  side  of  the  saw 
pointed  like  a  gouge,  with  two  .joint  dogs,  one  on  each  side  of  the  saw. 

Remedy  for  a  long  Pitman. 

Make  it  in  two  parts  by  a  joint  10  feet  from  the  crank,  and  a  mortise 
through  a  fixed  beam,  for  the  lower  end  of  the  upper  part  to  play  in,  the 
gate  will  work  more  steady,  and  all  may  be  made  lighter- 

The  feed  of  a  saw  mill  ought  to  be  regulated  by  a  screw  fixed  to  move 
the  hand-pole  nearer  or  farther  froni  the  centre  of  the  roller  that  moves  it, 
which  may  be  done  as  the  saw  arrives  at  a  knot  without  stopping  the  mill. 


END  OF  PART  FIFTH. 


APPENDIX, 

CONTAINING, 

Rules  for  Discovermg  New  Improvements  ^ 

EXEMPLIFIED  IN  IMPROVING 

THE  ART  OF  CLEANING  AND  HULLING  RICE, 

WARMING  ROOMS, 

AND 

VENTING  SMOKE  BY  CHIMNEYS,  §c. 


The  True  Paths  to  Inventions. 

NECESSITY  IS  called  the  mother  of  Inventions— but  upon  inquiry  we 
shall  fi  id,  that  Rt-ason  and  Expt-rimem  bring  them  forth— For  aimo-.!  all 
invent  ons  have  been  discovered  by  such  steps  as  the  following;  which 
aaay  be  taken  as  a 

RULE. 

STEP  I.  Is  to  investigate  the  fundamental  principles  of  the  theory,  and 
process  ot  the  art  or  manufacture  we  wish  to  improve- 

II.  To  consider  what   is  the   best  plan  in  theory  that  can  be  deduced 
from,  or  founded  on  those  principles  to  produce  the  effVct  we  desire- 
Ill.  Consider  whether  the  theory  is  already  put  in  practice  to  the  best 
advantage;   and  what  are  the  imperfections  or  disadvantages  of  the  com- 
mon process  improved,  and  what  plans  are  likely  to  succeed 

IV  Make  experiments  m  practice  to  'ry  any  plans  that  these  speculative 
reasonings  may  propose,  or  lead  to — Any  ingenious  artist,  taking  the  fore- 
going steps.  Will  probably  be  led  to  improvements  on  his  own  art  :  for  we 
see  by  daily  experience,  that  every  an  may  be  improved.  It  will,  how- 
ever, be  in  vain  to  attenipi  improvements  unless  the  mind  be  freed  from 
prejudice,  in  favour  of  established  plans. 

EXAMPLE  I, 

Take  the  Art  of  cleaning  Grain  by  fVind. 

BY  THE  RULE- 
STEP  I    What  are  the  principles  on  which  the  art  is  founded  ?    Bodies^ 
falling  through  resisiing   mediums,  their  velocities   are  as   their  specific 
gravities  ;  consequently  the  farmer  they  tall  the  greater  will  be  their  dis« 
tance  ;  on  this  principle  a  separation  can  be  effected- 


364  APPENDIX. 

II.  what  is  the  best  plan  in  theory  ?  First,  make  a  current  of  air  for  the 
grain  to  tall  throu^ch,  as  deep  as  possible  ;  then  the  lighiest  will  be  carried 
farthest,  and  the  separation  be  more  complete  at  the  end  of  the  tall-  Se- 
condly, cause  the  gran  with  the  chaff,  &c.  to  fall  in  a  narrow  line  across 
the  ciirrt-nt,  that  the  lighi  parts  may- nicirt  no  obsiruciion  from  the  ht-avjr 
in  being  carried  forward-  Third!),  fix  a  movea'-lt-  hoard  edgewise  to  se- 
parate between  the  good  clean  gra'h,  and  light  grain,  &c.  F  nr'hly,  cause 
the  s^me  blast  to  blow  the  grain  several  tiiiies,  and  thereby  effect  a  com- 
plete separation  at  one  opt-raiion. 

Ill-  Is  this  theory  in  practice  already  ?  what  are  the  disadvantages  of  the 
common  process  ?  We  find  that  the  f.-»rmers'  common  fans  drop  the  grain 
in  a  line  15  niclies  wide,  to  fall  through  a  <iirrt-ni  of  air  about  8  inches 
deep,  fins. e  id  of  tailing  in  a  Ime  half  an  inch  wide,  through  a  current  tliree 
feet  deep  )  So  that  it  requires  a  very  sirong  blast  even  to  blow  ou'  'he 
chaff;  but  garlic,  light  grains,  &c-  cannot  be  got  out,  they  meet  so  much 
obs' ruction  trom  tlie  heavy  grams-  It  h:is  to  undergo  iwo  or  three  opera- 
tions; so  that  the  practice  appears  no  way  equal  to  theory;  and  appears 
absurd  when  tried  by  the  scale  of  re.>son. 

IV.  The  fourth  step  is  to  construct  a  fan  to  put  the  tbeory  in  priictlce, 
to  try  the  experiment.*     See  Art.  83. 


EXAMPLE  II. 

Take  the  Art  of  Distillation. 

STEP  I.  The  principles  on  wh'ch  this  art  is  founded  are,  evaporation 
and  condensation.  The  liquid  being  heated,  ihe  spirit  it  contains  being 
most  oily  and  lightest,  evaporates  fiist  into  steam,  which  being  condensed 
again  into  liquid,  by  cold,  is  the  spirits. 

II.  The  best  plan  in  theory  for  effecting  this,  appears  as  follows:  the  fire 
should  be  applied  to  the  still  so  as  to  spend  the  greatest  part  of  its  heat 
possible,  to  heat  the  liquid.  Secondly,  the  steam  should  be  conveyed  int» 
a  metal  vessel  of  any  form  that  may  sui  best;  which  is  to  be  immersed  in 
cold  water,  to  condense  the  steam;  and  in  order  to  keep  the  condenser 
cold,  there  shoi-ld  be  a  stream  of  water  continually  entering  the  bottom 
and  flowing  over  the  top  of  the  condensing  tub,  the  steam  should  have  no 
free  passage  out  of  the  condenser,  else  the  strongest  part  of  the  liquor  may 
escape. 

Ill-  Is  this  theory  already  p'tt  in  practice,  and  what  are  the  disadvan- 
tages of  the  common  process  ?— 1st  Greatest  part  of  the  heat  escapes  up 
the  chimney.  2d.  It  is  almost  impossible  to  kef-p  the  grounds  froni  burn- 
ing in  the  still.  3dly.  The  fire  cannot  be  reguL.ted  to  keejAhe  still  from 
boding  over ;  therefore  we  are  obliged  to  run  slow:  to  remedy  these  dis- 
advantages—  First,  to  lessen  the  fuel,  apply  the  fire  as  much  to  the  surface 
of  the  still  as  possible  Enclose  the  fire  by  a  wall  of  clay  that  will  not  con- 
vey the  heat  awa\  so  fast  as  s'one  ;  let  m  as  little  a'r  as  possibly  can  be 
made  to  keep  the  fire  biiriiing  ;  for  the  air  carries  away  the  heat  of  the  fii-e. 
Secondly,  to  keep  the  grounds  from  bmning,  immerse  'he  still  with  the 
liquor  into  a  vessel  of  water,  joining  their  tops  together,  then  by  applying 
the  fire  to  heat  the  water  in  the  outside  vessel  the  grounds  v.ill  not  burn, 

•  This,  Timothy  Kirk,  carpenter,  of  York-town,  is  about  to  do,  and 
ckiims  the  invention  of  the  application  of  the  samp  blast  several  times,  so 
as  to  clean  the  grain  completely  ai  one  operation  ;  and  if  the  plans  are  well 
executed  will  no  doubt  excel  all  others  vet  made. 


APPENDIX.  56* 

and  by  regulating  the  heat  of  the  outside  vessel  the  still  may  be  kept  from 
boiling  over. 

IV.  A  still  of  this  structure  was  made  by  Colonel  Alexander  Anderson^ 
of  Philadelphia,  and  the  experinnent  tried  ;  but  the  water  in  the  outside 
vessel  boiled,  and  being  open,  the  heat  escaped  thereby>  and  '.he  liquor  in 
the  still  could  not  be  made  to  boil — this  appeared  to  defeat  the  scheme. 
B'lt  considering  that  by  enclosing  the  water  in  a  ti^ht  vessel,  so  that  the 
steam  could  not  escape,  and  that  by  compressure  the  heat  might  be  in- 
creased, and  it  passed  to  the  liquor  in  the  sliU,  which  now  boiled  as  well 
as  if  ihe  fire  had  been  immediaiely  applied  to  the  still.  Again,  by  fixing 
a  valve  to  be  loaded  so  as  to  let  the  sfeam  escape,  when  arrived  to  such  a 
degree  of  heat  as  to  be  near  boiling  over,  then  the  stili  could  not  be  iDade 
to  boil  over  at  all. 

Thus  was  an  improvement  produced,  by  which  he  can  despatch  business 
in  the  ratio  of  2  to  1,  expei.ding  fuel  in  the  ratio  of  2  to  2^,  to  produce 
equal  quantities  of  liquor. — We  may  bring  forward  another  improvement 
by  considering,  that,  as  we  know  by  experience  that  compressure  above 
the  weight  of  the  atmosphere,  keeps  the  stt^amfrom  rising  from  the  water, 
till  heated  to  a  certain  degree  above  the  boiling  heat.  We  may  hence  con- 
clude that  a  compressure  less  than  the  atmosphere,  will  suffer  it  to  rise 
wiih  a  degree  less  than  boiling  heat,  which  suggests  the  expediency  of  tak- 
ing off  the  pressure  of  the  atmosphere  from  the  liquor  in  the  still,  by  which 
means  we  shall  expend  less  fuel,  and  the  heat  need  never  be  so  great  as  to 
burn  the  grounds,  which  may  be  done  by  putting  the  end  of  the  worm  into 
a  light  globular  vessel  of  meial>  and  a  cock  between  it  and  the  condenser; 
then  inject  steam  from  a  small  boiler,  and  expel  all  the  air  out  of  this  ves- 
sel; turn  the  cock  and  it  will  run  into  the  condenser  and  be  condensed. 
By  repeating  this,  a  vacuum  may  be  easily  made,  and  kept  up  in  the  worm 
and  top  of  the  still,  and  the  spirits  will  probably  come  ofT  with  half  the 
heal  ard  fuel  usually  expended. 

Th:s  is  aboijt  to  be  put  in  practice  to  try  the  experiment.  Proved  to  be 
an  error  :  much  more  heat  is  required  to  bring  off  the  quantity  of  spirits. 
See  my  woik  on  Steam  Engines. 


EXAMPLE. 

Take  the  Art  of  Venting  Smoke  from  Roo772S  by  Chimneys. 

STEP  I.  The  principles  are: — Heat,  by  repelling  the  particles  of  air  to 
a  greater  distance,  being  lighter  titan  cold,  will  rise  above  it,  forming  a 
current  upwards,  with  a  velocity  proportional  lo  the  degree  and  quantity 
of  heat,  and  size  of  ihe  tube  or  funnel  of  the  chimney,  throu  h  which  it  as- 
cends, and  with  u  power  proportional  to  its  perpendicular  height,  which 
power  to  ascend  will  always  be  equal  to  the  difference  of  the  weight  of  a. 
column  of  rarefied  air  of  the  size  ut  the  smallest  part  of  the  chimney,  and 
a  column  of  common  air  of  eqial  size  and  height- 

II.  What  is  the  best  plan  in  theory  for  venting  smoke,  that  can  be  found- 
ed on  these  principles  ? 

1st.  The  size  of  the  chimney  must  be  proportioned  to  the  size  and  close- 
ness of  the  room  and  size  of  the  fire  ;  because,  if  the  chimney  be  immense- 
ly large  and  'he  fire  small,  there  <Aill  be  no  current  upwards.  And  again, 
if  the  fire  be  large,  and  the  chimney  too  small,  the  smoke  cannot  be  all 
vented  by  it,  more  air  being  noce^sai y  to  supply  the  fire  than  can  find  vent 
up  the  chimney,  it  must  spread  in  the  room  again,  which  after  passing 
through  the  fire  and  being  burnt  is  suffocating. 


a66  APPENDIX. 

2d.  The  narrowest  place  in  the  chimney  must  be  next  the  fire,  and  ia 
front  of  it,  so  that  the  smoke  would  have  to  pass  under  it  to  get  into  the 
room  :  the  current  will  there  be  greatest,  and  will  draw  up  the  smoke 
briskly- 

3d,  The  chimney  must  be  perfectly  tight,  so  as  to  admit  no  air  but  at 
the  bottom. 

Ill-  The  errors  in  chimneys  in  common  practice  are, 

1st-  In  making  them  widest  at  bottom. 
•     2d    Too  large  for  the  size  and  closeness  of  the  room. 

3d.  In  not  building  them  high  enough  above  the  wind  whirling' over  the 
tops  of  houses,  that  blow  down  them. 

4th.  By  letting  in  air  any  where  near  the  bottom,  destroys  the  current 
of  it  at  bottom. 

IV.  The  cures  directed  by  the  principles  and  theory  are, 

1st.  If  the  chimney  smoke  on  account  of  being  too  large  for  the  size  and 
closeness  of  the  room,  open  a  door  or  a  wmdow,  and  make  a  large  fire. 
But  if  this  be  too  expensive,  make  the  chimney  less  at  the  bottom — its 
size  at  the  top  will  not  be  much  injury,  but  will  weaken  the  power  of  as- 
cent, by  giving  the  smoke  time  to  cool  before  it  leaves  the  chimney:  the 
room  may  be  as  tight,  and  fire  as  small  as  you  please,  if  the  chimm-y  be  in 
proportion* 

2d.  If  it  be  small  at  the  top  and  large  at  the  bottom,  there  is  no  cure  but 
to  lessen  it  at  the  bottom. 

3d.  If  it  be  too  small,  which  is  seldom  the  case,  stop  up  the  chimney 
and  use  a  stove — it  will  be  large  enouj^^h  to  vent  all  the  air  that  can  pass 
through  a  two  inch  hole,  which  is  large  enough  to  kindle  the  fire  in  a 
stove-*  The  chimneys  built  to  put  these  theories  in  practice  I  believe  are 
every  vxhere  found  to  answer  the  purpose.  See  Franklin's  letters  on 
smoky  chimneys. 

EXAMPLE  IV. 


Take  the  Art  of  Warming  Rooms  by  Fire. 

STEP  I.  The  principles  of  fire  are  too  mysterious  to  be  investigated 
here  -,  but  the  effects  are, 

1st.  The  fire  ratifies  the  air  in  the  room,  which  gives  us  the  sensation 
of  heat  or  warmth. 

2d.  The  warmest  part  being  lightest,  rises  to  the  uppermost  part  of  the 
room,  and  will  ascend  through  holes  (if  there  be  any)  to  the  room  above, 
making  it  warmer  than  the  one  in  which  the  fire  is. 

3d.  If  the  chimney  be  open  the  warm  air  will  fly  up  it  first,  leaving  the 
room  empty,  the  cold  air  will  then  rush  in  at  all  crevices  to  supply  its 
place,  which  keeps  the  room  cold. 

II.  Considering  these  principles,  what  is  the  best  plan  in  theory  for 
warming  rooms  ? 

1st.  We  must  contrive  to  apply  the  fire  to  spend  all  its  heat,  to  warm  the 
air  as  it  comes  in  the  room- 

2d.  To  retain  the  warm  air  in  the  room,  and  let  the  coldest  out  first  to 
obtain  a  ventilation. 

3d.  Make  the  fire  in  a  lower  room,  conducting  the  heat  through  the  floor 

•  The  quantity  of  fuel  necessary  to  warm  a  room,  will  ever  be  in  propor- 
tion to  the  quantity  of  air  that  ascends  the  chimney. 


APPENDIX.  367 

into  the  upper  one,  and  leaving  another  hole  for  the  cold  air  to  descend  to 
the  li/wer  rf)()m 

4ih  M.iktr  the  roonn  perfectly  tight  so  as  to  admit  no  cold  air,  but  all 
warmed  js  it  comes  m. 

5'h  By  stopping  up  the  chimney  to  lei  no  warm  air  escape  up  it,  but 
what  is  absoliUfly  ne.:essary  to  kindle  thefiie — a  hole  of  two  square  inch- 
es will  be  sufficient  for  a  very  large  room. 

6rh.  The  fire  may  be  kindled,  by  a  current  of  air  brought  from  wlhout, 
noi  using  uny  of  the  air  already  warmed.     If  this  theory,  which  is  found-" 
ed  on  true  principles  and  reason,  be  compared  with  common  practice,  the 
errors  will  appear— ihe  disadvantaj^es  of  which  may  be  evaded. 

III.  I  had  a  stove  consM-ucted  to  put  this  theory  as  fjlly  in  practice  as 
possible,  and  have  found  all  'o  answer  according  to  theory. 

The  operation  and  effects  are  as  follows,  viz. 

1st.  It  applies  the  fire  to  warm  the  air  as  it  enters  the  room,  and  admits 
a  full  and  fresh  supply,  rendering  the  room  mod'  ra'ely  warm  ihroughnut. 

2d.  It  effectual  y  prevents  the  cold  air  from  p:essing  in  at  the  clunks  or 
crevices,  but  causes  a  small  current  to  pass  ou'wards. 

3d.  It  conveys  the  coldest  air  out  of  the  room  first,  conseqiiently, 

4th.  It  is  a  complete  ventilator,  thereby  renderir.g  the  irxirti  healihy. 

5th.  The  fire  m;iy  be  supplied  (in  very  cold  wi  a>li(-r)  by  a  current  of  air 
from  without,  that  dOfS  not  communic.-te  with  the  warm  air  in  the  room. 

6th.  Warm  air  may  be  ret-ined  in  the  room  any  lengt  of  time,  at  plea- 
sure ;  circulating  through  the  stove,  the  coldest  entering  first  to  be  warm- 
ed over  again  * 

7th.  It  will  bake,  roast,  and  boil  equally  well  with  the  common  ten  plate 
stove,  as  it  has  a  capacious  oven. 

8'h.  In  consequence  of  these  philosophical  improvements,  it  requires  not 
more  than  half  the  usual  quantity  of  fuel. 

Description  of  the  Philosophical  and  Ventilating  Stove. 

It  consists  either  of  three  cylindric  or  square  parts,  the  greatest  sur- 
rounding the  least.  See  plate  X.  fig.  1.  SF  is  a  perspective  view  hereof 
in  a  square  form,  supposed  open  at  one  side  :  the  fire  is  put  in  at  F,  in  the 
least  part  which  comiiiunicates  with  the  space  next  the  outside,  wliei  e  i  he 
smoke  passes  to  the  pipe  1 — 5.  The  middle  part  is  about  two  mclit-s  U  ss 
than  the  o-'tside  part,  leaving  a  large  space  between  it  and  above  ihe  in- 
ner part  for  an  oven,  in  which  the  air  is  warmed,  being  brought  m  by  a  pipe 
B  D  between  the  joists  of  ll.e  floor,  from  a  hole  in  the  w  all  ai  B,  ns  ng  mto 
the  stove  at  U,  in'o  the  space  -ind  oven  sunocnding  the  fire,  which  air  is 
again  surrounded  by  the  smoke,  giving  the  fire  a  fuil  a  .ion  to  waim  it, 
and  ascending  into  tiie  room  by  ihe  pipe  2-  K  brings  air  from  itit  p  pa 
DB  to  blow  the  fire.  II  is  a  view  of  the  front  end  piate,  show.ng  the  fire 
and  oven  doors  I  is  a  view  of  the  back  end,  the  plate  bein,,  off,  tlif.  uark 
sqiare  shows  the  space  for  the  fire,  and  the  light  part  the  air  space  vur- 
rounding  the  fire»  the  dark  outside  space  the  smoke  surrounding  the  air; 
these  are  drawn  on  a  larger  scale.  The  stove  consists  of  15  plates,  12  of 
which  join  one  end  against  the  front  plate  H. 

To  apply  'his  stove  to  the  best  advantage,  suppose  fig-  1,  pla  e  X.  to  re- 
present a  three  or  four  story  house,  two  rooms  on  a  floor — set  ihe  stove  SF 


•  This  application  was  suggested  to  me  by  Isaac  Garret  son,  of  York- 
town,  on  his  viewing  the  stove  and  considering  its  principles  whilst  I  had 
it  m^tng. 


368  APPENDIX. 

in  the  partition  on  the  lower  floor,  half  in  each  room ;  pass  the  emoke  pipe 
throui^h  all  the  stories:  make  the  room  very  close ;  let  no  air  enter  but 
what  comf  s  in  by  the  pipes  A  B  or  CC  through  the  wall  at  A  and  G,  that  it 
may  be  the  more  pure,  and  pass  through  the  stove  and  be  warmed.  But 
to  convey  it  to  any  room,  and  take  as  m>ich  heal  as  possible  with  it,  there 
must  be  an  airpipe  surrounding  the  smoke-pipe,  with  a  valve  to  open  at 
every  floor.  Suppose  we  wish  to  warm  the  rooms  No.  3 — 6,  we  open  the 
valves,  and  the  warm  air  enters,  ascends  to  the  upper  part,  depresses  the 
cold  air,  and  ii  we  open  the  holes  a — c  it  will  descend  the  pipes,  and  enter 
the  stove  to  be  warmed  again  :  this  may  be  done  in  very  cold  weather.  The 
higher  the  room  above  the  stove,  the  more  powerfully  will  the  warm  air  as- 
cend and  expel  the  cold  air.  But  if  the  room  requires  to  be  ventilated, 
the  air  must  be  prevented  from  descending,  by  shutting  the  little  gate  2  or  5, 
and  drawing  1  or  6,  and  giving  it  liberty  to  ascend  and  escape  at  A  or  G — or 
up  the  chimney,  letting  it  m  close  at  the  hearth.  If  the  warm  air  be  con- 
veyed  under  the  floor,  as  between  5 — 6,  and  let  rise  in  several  places,  with 
a  v.ilve  at  each,  it  would  be  extremely  convenient  and  pleasant ;  or  above 
the  floor  as  at  4 — several  persons  might  set  i.heir  feet  on  it  to  warm.  The 
rooms  will  be  moderately  warm  throughout — a  person  will  not  be  sensible 
of  ihe  coldness  of  the  weather. 

One  larije  stove  of  this  construction  may  be  made  to  warm  a  whale 
house,  ventilate  the  rooms  at  pleasure,  bake  bread,  meat,  &c. 

These  principles  and  improvements  ought  to  be  considered  and  provid- 
ed  for  in  bulding. 

EXAMPLE  V. 


Take  the  Art  of  Hulling  and  Cleaning  Rice, 

STEP  I.  The  principles  on  which  this  art  may  be  founded  will  appear 
by  taking  a  handful  of  rough  rice,  and  rubbing  it  hard  between  the  hands 

the  hulls  will  be  broken  off,  ;<nd  by  continuing  the  operation  the  sharp 

text:  re  of  the  outside  of  the  hull  (which  through  a  magnifying  glass  ap- 
peavs  like  a  sharp  fine  file,  and  no  doubt  is  designed  by  nature  for  the  puijj 
pose)  will  cut  off  the  inside  hull,  the  chaff  being  blown  out,  will  leave  the 
rice  perfectly  clean,  without  breaking  any  of  the  grains. 

11  What  is  the  best  plan  in  theory  for  effecting  this  ? — See  the  plan  pro- 
posed, represented  plate  X  fig  2 — explained  art.  103. 

Ill-  The  disadvantages  of  the  old  process  are  known  to  those  who  have 
it  to  dO' 

EXAMPLE  VL 

To  Save  Ships  from  Sinking  at  Sea. 

STEP  I-  The  principles  on  which  ships  float,  is  the  difference  of  their 
specific  gravities  from  that  of  the  water,  bulk  for  bulk— sinking  only  to 
displace  water  equal  in  weight  to  the  ship;  therefore,  they  sink  deeper  in 
fresh  than  salt  water.  If  we  can  calculate  the  cubic  feet  a  ship  displaces 
when  empty  it  will  show  her  weight,  and  subtracting  that  from  what  she 
di  places  when  loaded,  shows  the  weight  of  her  load,  each  cubic  foot  of 
frtsh  water  being  62,5lb.  If  an  empty  rum  hogshead  weigh  62,51b.  and 
measure  15  cubic  feet,  it  will  require  875  lb.  to  sink  it.    A  vessel  of  iron. 


APPENDIX.  369 

&c.  filled  with  air,  so  large  as  to  make  its  whole  bulk  lighter  than  so  much 
water,  will  float,  but  if  the  air  be  let  out  and  filled  with  water,  will  sink. 
Hence  we  may  conclude  that  ships,  loaded  with  any  thing  that  will  float. 
Will  not  sink,  if  filled  with  water;  but  if  loaded  with  any  thing  specifically 
heax'ler  th^n  water,  will  sink  as  soon  as  filled. 

II  This  appears  to  be  the  true  theory — How  is  it  to  be  put  in  practice, 
in  case  a  ship  springs  a  leak,  that  gains  on  the  pumps  ? 

III.  The  mariner  who  understands  well  the  above  principles  and  theory, 
will  be  led  to  the  following  steps. 

1st.  To  cast  overboard  such  things  as  will  not  float,  and  carefully  to  re- 
serve every  thing  that  will  float,  for  by  them  the  ship  may  be  at  last  buoy- 
ed up. 

2d.  Empty  every  cask  or  thing  that  can  be  made  water-tight,  and  put 
them  in  the  hold  and  fasten  them  down  under  the  water,  filling  the  vacan- 
cies between  them  with  billets  of  wood;  even  the  spars  and  masts  may  be 
cut  up  for  this  purpose  In  desperate  cases,  which  will  fill  the  hold  with  air 
and  light  matter,  and  as  soon  as  the  water  inside  is  level  with  that  outside, 
no  more  will  enter.  If  every  hogshead  buoy  up  8751b.  they  will  be  a  great 
help  to  buoy  up  the  ship,  (but  care  must  be  taken  not  to  put  the  empty 
casks  too  low,  which  wo'dd  overset  the  ship)  and  she  will  float,  although 
half  her  bottom  be  torn  off.  Mariners,  for  want  of  this  knowledge,  often 
leave  their  ships  too  soon,  taking  to  their  boat,  altliough  the  ship  is  much 
the  safest,  and  does  not  sink  for  a  long  time  after  being  abandoned — not 
considering,  although  the  water  gain  on  their  pumps  at  first,  they  may  be 
able  to  hold  way  with  it  when  risen  to  a  certain  height  in  the  hold,  be- 
cause the  velocity  with  which  it  will  enter,  will  be  in  proportion  to  the 
square  root  of  the  diflference  between  the  level  of  the  water  inside  and  out- 
Bide — added  to  this,  the  fuller  the  ship  the  easier  the  pumps  will  work, 
tberetore  they  ought  not  to  be  too  soen  discouraged. 


EXAMPLE  VII. 

Take  the  Art  of  Preserving  Fruits,  Liquor s,  ^c.  from 
Putrefaction  and  Fermentation. 

STEP  I.  What  are  the  principles  of  putrefaction  and  fermentation  ?  By 
experiments  with  the  air-pump  it  has  been  discovered  that  apples,  cher- 
ries, &c.  put  in  a  tight  vessel,  having  the  air  pumped  out,  wdl  keep  their 
natural  fresh  bloom  for  a  long  time-  Again,  by  repeated  experiments  it 
is  proved  things  frozen  will  neither  putrify  nor  ferment  while  in  that  state. 
Hence  we  may  conclude  that  air  and  heat  are  the  principles  or  moving 
causes  of  putrefaction  and  fermentation. 

II.  What  plans  in  theory  are  most  likely  to  succeed  ?  By  removing  the 
causes  we  may  expert  to  evade  the  effect- 

1.  Suppose  a  cistern  m  a  cellar  be  made  on  the  side  of  a  hill,  and  sup- 
plied by  a  spring  of  cold  water  running  in  at  the  top,  that  can  be  drawn  off" 
at  the  bottom  at  pleasure.  If  apples,  &c.  be  put  in  tight  vessels,  and  the 
air  pumped  out,  and  beer,  cider,  &c.  be  put  m  this  cistern,  and  immersed 
in  water,  will  they  putrify  or  ferment  I  May  not  the  experiment  succeed 
in  an  ice-house,  and  fruits  be  conveyed  from  one  country  to  another  in  glass 
or  metal  vessels  made  for  the  purpose,  with  the  air  pumped  out  and  her- 
metically sealed. 

In  support  of  this  hypothesis,  a  neighbour  of  mine  told  me,  he  filled  a 
rum  hogshead  in  the  fall  full  of  apples  at  the  bung,  bunged  it  tight,  and  in 

3    A 


370  APPENDIX. 

the  spring  found  them  all  sound ;  another,  when  a  hoy,  buried  a  hollow  ^in 
bee  hive  full  ot  apples,  trampled  the  earth  tight  about  tliem,  opened  tliem 
when  the  wheat  bei^an  to  npen,  and  found  them  all  sound,  but  leaving 
thenn,  returned  in  a  day  or  two,  and  found  them  all  rotten* 


I^or  those  who  Bead  to  have  Leisure. 

BY  the  right  use  of  Natural  Philosophy  and  Reason,  aided  by  Experi- 
nienis,  m:^ny  im|)rovements  might  be  made  thai  would  add  much  to  the 
conveniences  and  comforts  of  lite-  But  the  great  obstacle  is  the  expense 
of  experiments,  in  reducing  theory  to  practice,  which  tiew  will  risk-  For 
when  a  man  attempts  to  m^ike  any  improvements,  he  is  sure  to  be  ridiculed 
until  he  succeeds,  and  then  the  invention  is  often  depreciated — Dr.  Frank- 
lin said— that  "a  man's  useful  inventions  subject  him  to  insult,  robbery, 
and  abuse" — but  this  I  have  as  yet  experienced  only  from  two  or  three  in- 
dividuals from  whom  it  was  least  to  be  expected-  I  am  firmly  persuaded, 
that  if,  in  iuy  country,  the  small  sum  of  ■   dollars  annually,  was  aa-> 

signed  to  red  <ce  to  practice  probable  iheonts,  the  arts  would  rise  in  im- 
provement beyond  any  precedent  that  history  can  evince;  and  the  power 
and  wealth  of  the  nation  in  pi-oportion — For  a  long  list  of  inventions  la 
theory  might  be  given,  that  offer  fair  to  be  very  useful  in  practice,  that  lie 
dormant  until  the  inventor  can  make  experiments  with  convenience,  to  re- 
duce them  to  practice — many  of  which,  no  doubt,  will  die  with  the  inven- 
tors. 

Sensible  of  the  expense,  time,  labour,  and  thought,  that  this  (though 
small)  work  has  cost  me,  and  hoping  it  may  be  well  received  by,  and  prove 
serviceable  to,  my  country — 1  wail  to  see  its  fate ;  and  feel  joy  in  being 
ready  to  say — FINIS. 

•  Much  contained  In  this  Appendix  is  to  be  found  in  different  authors; 
and  several  things,  which  I  thought  bad  originated  with  myself,  have  been 
treated  of  by  Dr-  Franklin. 


APPENDIX.  S7l 


COMMUNICATION. 


The  following  Essay  on  Saw-Mills^  &c.  I  receiv- 
ed from  William  French,  Mill-wright^  Bur- 
lington  county^  (JVew  Jersey.)  si?ice  I  concluded, 
and  fearing  I  may  not  have  another  opportunity, 
I  publish  it, 

SAW-MILLS  have  been  much  improved  in  this  state,  for  low.heads» 
Mills  wi'h  two  saws,  with  not  more  than  7  feet  head  and  fall,  have  sawed 
5  and  6  hundred  thousand  feet  o>  board:>,  plunk,  and  scantlmg,  in  one  year. 
If  (he  w^-ter  be  put  on  the  wheel  in  a  proper  manner,  and  the  wh  el  of  a 
proper  size,  (as  by  the  following  table)  the  sa«  will  strike  between  100 
and  130  strokes  in  a  minute  :  see  fig.  I,  plate  XIV-  The  lower  edge  of  the 
breasi-beam  B  to  be  3  4  the  height  of  the  wheel,  and  one  inch  'o  a  toot, 
slanting  up  stream,  fastened  to  the  penstock-pos's  wuti  screw-bolts,  (see 
post  A)  circled  out  to  s'lit  the  wheel  C;  the  tall  D  circled  to  soit  the 
wheel  and  extended  to  F,  2  inches  above  the  lower  edge  of  the  breast- 
beam,  or  higher,  according  to  the  size  of  the  throat  or  slnice  E.  with  a 
shuttle  or  gate  sliding  on  FE,  shutting  against  the  breast-beam  B:  then 
4  buckets  0'>t  of  9  will  be  acted  on  by  the  water-  The  method  of  fasten- 
ing thf  buckets  or  floats  is,  to  step  them  in  starts  mortised  in  ibe  sh^fi-^ 
see  start  G— 4  buckets  in  a  wheel  4^  inches  wide,  see  them  numbered 
1,  2,  &c. 

Fig.  2,  is  the  go-back,  a  tub-wheel.  Its  common  size  is  from  4^  to  6  feet 
diameter,  with  16  buckets-  The  water  is  brought  on  it  by  tlie  trunk  H. 
The  bucket  I  is  made  with  a  long  tenon  so  as  to  fasten  it  with  a  pin  al  the 
top  of  the  wheel 

TABLE 

Of  the  Dimensions  of  Flutter-wheels. 


Head  12  feet- 

Bucket  5  feet. 

Wheel  3  feet. 

Throat  1  3-4  inch 

11 

512 

3 

2 

10 

6 

3 

2  18 

9 

61-2 

2  10  inches 

21  4 

8 

7 

2    9 

212 

7 

71-2 

2    8 

314 

6 

8 

2    7  p. 

312 

5 

9 

2    6 

3  3  4' 

N'.  B.  The  crank  about  11  inches,  but  varies  to  suit  the  timber. 


372  APPENDIX. 


The  Pile  Engine. 

Fig-.  3,  a  simple  machine  for  driving  piles  in  soft  bottoms  for  setting 
mill-walls  or  dams  on.  It  consists  of  a  frame  6  or  7  feet  square,  of  scani- 
linef,  4  by  5  inches,  with  2  upright  posts  2  inches  apart,  10  or  12  tee«  high, 
3  bj  3  Inches,  braced  from  top  to  bottom  of  the  frame,  with  a  cap  on  'op  2 
feet  long,  6  by  8  inches,  with  a  pulley  in  its  middle,  for  a  ropp  to  bend  over 
fastened  to  a  block  I,  called  a  tup,  which  has  2  pieces  4  inches  wide  be- 
tween the  uprights,  with  a  piece  of  2  inch  plank  T,  6  inche<  wide,  fr;inied 
on  the  ends,  so  as  to  slide  up  and  down  the  upright  posts  S-  This  machme 
is  worked  by  4  or  6  men,  drawing  the  tup  up  by  the  sticks  fastened  to  the 
end  of  the  rope  K,  and  letting  it  fall  on  th.  pde  L :  they  can  strike  30  or 
10  strokes  by  the  swing  of  their  arms  in  a  minute- 

Of  building  Dams  on  Soft  Foundations. 

The  best  method  is  to  lay  3  sills  across  stream,  and  frame  cross  sills  in 
them  up  and  down  stream,  setting  the  main  mudsills  on  round  pdes,  and 
pile  them  with  2  inch  plank,  well  jointed  and  drove  close  together  edge 
to  edge,  from  one  to  the  oilier  end-  By  taking  one  corner  off  the  lower 
end  of  the  plank  will  cause  it  to  keep  a  close  joint  at  boliom,  and  by  driv- 
ing an  iron  dog  in  the  mud-sill,  and  a  wooden  wedge  to  keep  it  close  at 
the  top  end  will  hold  it  to  its  place  when  the  tup  strikes-  Ii  is  necessary 
to  pile  the  outside  cross  sills  also  in  some  bottoms,  and  to  have  wings  to  run 
10  or  12  feet  into  the  bank  at  each  side;  and  the  wing-posts  2  or  3  feet 
higher  than  the  posts  of  the  dam,  where  the  water  falls  over,  planked  to 
the  top  NN,  and  filled  with  dirt  to  the  plaie  O. 

Fig.  4,  IS  a  front  view  of  the  breast  of  the  t'mbling  dam- 
Fig.  5,  is  a  side  view  of  the  frame  of  the  tumbling  dam,  on  its  piling  a  b 
c  d  e  and  f  g  h  is  the  end  of  the  mud  sills.  The  posts  k  are  framed  into 
the  main  mud-sills  with  a  hook  tenon,  leaning  down  stream  6  inches  in  7 
feet,  supported  by  the  braces  1 1,  framed  in  the  cross  sills  I;  the  cross  sills 
I  to  run  25  feet  up  and  down  stream,  and  be  well  planked  over ;  and  the 
breast-posts  to  be  planked  to  the  top  (see  P,  fig-  4,)  and  filled  with  dirt  on 
the  upper  side,  within  12  or  18  inches  of  the  plate  O ;  (sei:-  Q,  fig.  5,)  slant- 
ing to  cover  tlie  up  stream  ends  of  the  sills  3  or  4  feet  deep  :  R  represents 
the  water. 

When  the  heads  are  high  it  is  best  to  plank  the  braces  for  the  water  to 
run  down,  but  if  low,  it  may  fall  perpendicularly  on  the  sheeting. 


I  THINK  it  my  duty  to  embrace  this  opportunity,  once  more  to  at- 
tempt at  drawing  the  attention  of  my  fellow-citizens,  to  the  most  ruinous 
error  tliat  the  supreme  legislature  of  my  country  has  commiited,  viz  The 
laws  do  not  protect  the  inventors  of  useful  improvements  in  the  arts,  in  the 
exclusive  enjoyment  of  the  fruits  of  their  labour,  for  a  s.fficient  length  of 
time,  nor  afford  them  any  adequate  compensation,  but  make  them  common 


APPENDIX.  373 

to  all  at  the  end  of  14  years ;  a  time  barely  sufficifeht  to  mature  (in  this 
country)  any  useful  improvement.    The  consequence  is,  the  inventor  is  de- 
luded by  the  name  of  a  patent,  and  his  hopes  raised  by  the  accounts  he  has 
heard  of  the  success  of  inventors  in  England,  and  he  makes  great  exertions 
and  sacrifices  to  mature,  and  introduce  into  use,  his  improvements;  but 
just  us  he  begins  to  receive  compensation  his  patent  expires,  his  sanguine 
hopes  are  all  blasted,  he  finds  himself  ruined,  and  conceives  that  he  has 
been  robbed  by  law,  is  thrown  into  despair,  and  tempted  to  deem  the  pre- 
cious gift  of  God  (rendering  him  useful  to  his  country)  as  a  curse;  his  chil- 
dren that  n»ay  receive  the  same  gift,  bury  their  talents  to  shun  the  danger. 
Thanks  to  the  Divine  Disposer  of  Events,  I  have  narrowly  escaped  the 
worst  part  of  this  general  fate,  having  had  prudence  sufficient  to  suppress 
(with  murh  difficulty)  my  great  desire  of  putting  into  operation  the  many 
useful  improvements  and  discoveries  that  opened  clearly  on  my  mind,  so 
far  as  to  attend  to  carrying  on  some  regular  business  for  the  support  of  my 
family,  and  defrslying  the  expense  of  my  experiments,  at  the  same  time 
that  my  mind  was  principally  employed  in  the  investigation  of  principles, 
and  inventing  useful  improvements.     I  am  however  free  to  declare,  that 
all  my  study,  labour,  and  time  expended  during  the  most  vigorous  half  of 
my  life,  in  making  new  inventions,  &c.  I  account  as  lost  to  myself  and  fa- 
mily, excepting  the  time,  &c.  expended  in  compiling  and  publishing  this 
work,  the  exclusive  right  of  selling  which,  is  by  law  secured  to  me  for  a 
second  term  of  14  years.     Two  years  ago  I  totally  relinquished  all  pursuit 
of  new  improvements,  and  there  is  nothing  more  irksome  to  me  at  present, 
than  »o  be  troubled  with  the  description  of  any  proposed  new  improve- 
ments, or  to  be  asked  for  my  opinion  or  advice  concerning  them  ;  and 
I  do    request  the  reader,  to  refrain  from  intruding  in  the  least  on  my 
time  in  that  way,  either  by  written  or  verbal  commnnications,  and  I  do 
further  declare  that  I  do  verily  believe,  that  had  the  laws  been  such  as  to 
ensure  adequate  compensation,  I  could  in  the  time  already  past,  have  in- 
vented and  introduced  into  use  other  improvements  that  would  have  prov- 
ed ten  times  as  beneficial  to  my  country,  as  all  those  which  I  have  accom- 
plished ;  but  I  have  been  forced  to  bury  my  talent  with  disgust ;  and  have 
bound  in  a  bundle  the  drawings  and  specifications  of  my  inventions,  which 
I  have  discovered  and  matured,  ready  for  putting  into  operation,  at  the  ex- 
pense of  the  most  intense  study  and  labour  of  the  mind,  resolving  never  to 
open  them,  until  the  laws  make  it  my  interest,  or  their  own,  to  do  so;  be- 
cause a  patent  in  this  country  is  not  yet  worth  the  expense  of  obtaining 
it. 

If  I  did  believe  that  these  declarations  would  only  tend  to  damp  the  ar- 
dour of  the  American  genius,  far  would  it  be  from  me  to  make  them>  (in 
this  I  may  indeed  have  erred  :)  but  looking  forward  to  futurity  I  contem- 
plate a  contrary  effect;  (worse  the  case  cannot  be  made — the  ardour  of  all 
prudent  men  has  long  ago  been  sufficiently  damped,  to  prevent  them  from 
engaging  in  such  pursuits.)  >Joihing  but  such  a  statement  of  real  facts,  in 
plain  truth,  will  rouse  the  attention  of  our  legislators  to  a  revision  of  the 
laws,  so  as  to  protect  inventors,  as  well  as  other  classes  of  the  community, 
in  the  enjoyment  of  the  fruits  of  their  labours,  for  a  sufficient  length  of 
time,  to  remunerate  them  for  their  time  and  labour,  and  reward  them  for 
their  perseverance  and  ingfenuily,  in  proportion  to  the  benefits  they  render 
their  country;  which  alone  can  inspire  them  with  renewed  hope,  and  give 
new  spring  to  genius  ;  for  it  is  absurd  to  suppose  that  any  prudent  man 
will  labour  for  property  which  he  must  surrender  by  law,  often  before  he 
can  fully  acquire  it,  or  that  expensive  experiments  should  be  made  with- 
out  hopes  of  reward.  But  if  congress  will  extend  the  patent  term  to  a  pe- 
riod that  will  ensure  adequate  compensation,  and  change  the  present  road 
to  rtiin  and  disgrace,  (in  which  none  but  the  imprudent  will  walk,)  to  a 
path  leading  to  wealth  and  honour,  they  will  soon  see  many  prudent,  inge- 


3/4  APPENDIX. 

nious  men  walking  therein  ;  and  the  arts  will  improve  with  a  progress  more 
raptd  than  hitlierto  known  in  any  country,  and  arrive  *'  a  greater  de^^ree  of 
perfection  in  half  a  century,  than  in  a  thousand  years  under  the  present 
discouraging  system  of  lepal  robbery.  Then,  mstead  of  discoveries  tjemg 
suppressed,  they  wdl  be  put  in  operation,  and  the  good  people  will  receive 
tile  benefits. 

I  wish  not  to  be  understood  to  have  relinquished  the  pirsuit  of  improve- 
ments on  the  business  I  may  follow,  or  in  ♦he  application  o''  my  new  prin- 
ciple to  steam  rngmes,  which  I  have  patentedr;  no,  this  'oven'ion  is  already 
accomplish,  d,  and  lam  striving  to  make  the  hest  of  it  during  my  patent 
term — 1  make  steam  engines  which  will  work  with  a  power  of  lOOI'-s  to 
the  inch  area  of  the  work  piston  ;  one  of  eight  inches  diameter  to  carry  a 
load  of  5000  ib.  when  required  in  extraordinary  cases.  This  is  ihv  ■  nly 
principle  whcb  will  apply  to  propel  boats  against  the  current  of  the  Mis- 
sissippi by  steam,  and  it  may  be  much  improved  on  in  its  application  for 
that  purpose ;  ali  attempts  without  it  will  fad  to  be  useful,  because  'here 
is  no  other  principle  in  nature  left,  that  will  serve  as  a  substitute.  When 
those  improvements  shall  be  made  in  the  application  of  this  principle,  and 
shall  be  put  in  full  operation  to  navigate  that  great  commercial  river,  then 
will  the  absurdityof  that  penurious  system,  which  has  ftl.-eadykept  backthis 
great  and  useful  discovery  for  upwards  of  twenty  years,  mos^  glarin  .ly  ap- 
pear. Let  a  calculator  si  down  to  conpute  the  anniial  btnefits  iha  w-U 
arise  to  the  people,  and  he  will  be  astonished  at  the  many  m  llionsof  dol- 
lars  that  will  appear  as  ihe  result.  This  calculation  I  refrain  from  slating, 
because  I  believe,  chat  most  of  my  readers  would  supi>ose  me  deranged. 
The  truth  will  not  bear  to  be  told  m  this  case,  even  lo  those  whose  local 
situation  is  such,  that  they  would  be  raosi  bei'efi'ted 

For  a  full  explanation  ot  my  improvt  ment  on  steam  engines,  see  my  new 
work,  entitled,  "The  .\bortion  of  the  Young  Ste<m  Engineer's  Guide.** 
Price  125  cents.  I  am  well  prepared  to  construct  stea.ii  engines,  on  short 
notice  for  those  who  may  want  them:  they  will  serve  as  a  substitute  for 
water  falls,  with  great  advantage,  where  fuel  is  pi'  nty.  I  have  established 
works  for  the  purpose,  consisting  of  an  iron  foundry,  ste^m  engineer's 
shop,  mould  maker's  shop,  steam  mill  for  turning  and  boring  heavy  iron 
work,  and  a  blacksmith's  shop,  all  connected:  Also,  a  m'U-sion  manufac- 
tory'—and  am  prepared  to  execute  all  orders  th^t  I  may  receive  in  either 
of  the  above  lines,  especially  for  ensfine  and  mill-woi  ks,  of  either  cast  or 
wrought  iron-    Apply  at  Mars's  Works,  Philadelphia. 


THE  END. 


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